Index

achievable rate region, 409 adder channel, 49 Agnew, G. B., 1 Ahlswede, R., 13 algebraic decoding, 72 algorithm

Berlekamp-Massey, 72, 209, 211, 288,307 Berlekamp-Welch, 217 Cooley-Tukey, 144 Coppersmith, 223 Euclidean, 211 Fano, 73 gradient, 358, 360 Good-Thomas, 144 Lanczos, 213 Lempel-Ziv, 431 Levinson, 209, 215 Minty, 116 Schur, 209, 216 Stack, 453 Sugiyama, 211 Viterbi, 73, 116, 120, 124, 158,201, 399,449

amplitude modulation, 71 aperiodic autocorrelation function, 381 authentication, 273

Barker sequence, 326, 381 base station, 129, 423 baseline wander, 173 BCH code, 43, 72, 141 Berlekamp, E., 25 Berlekamp-Massey algorithm, 35, 72, 209, 211, 288, 307 Berlekamp-Welch algorithm, 217

461

binary entropy function, 451 binary multiplying channel, 56 binary sequence, 381 binary symmetric channel, 157,251, 259 binomial coefficient, 142 biorthogonal code, 72 birthday paradox, 222 bit error rate, 72 Blackburn, S., 35 Blahut, R. E., 43 Blahut's theorem, 49, 141, 149 Blake,1. F., 49 block code, 56, 116, 201 blowing up lemma, 55 bound

Elias, 400 Hamming, 251 Heller, 400 Levenshtein, 110 Odenwalder, 400 Plotkin, 400 random-coding, 251 Singleton, 95 Varshamov-Gilbert, 204, 251, 255, 450

bounded distance decoding, 391,392 broadcast channel, 271,353,409 broadcast protocol, 13 burst error correcting, 252

capacity, 69, 82, 316 capacity region, 50, 410 Carter, G., 35 cascading, 155 catastrophic error propagation, 399 Cayley-Hamilton theorem, 368

CDMA system, 134 channel

adder, 49 broadcast, 271, 353,409 collision, 353, 419 interference, 409 multiaccess, 49, 81, 315, 409

channel coding theorem, 69 charge constrained convolutional code, 173 cipher

IDEA, 227 PES, 227 Rip Van Winkle, 179

circuit theory, 216 code

BCH, 43, 72, 141, 209 concatenated, 206 constacyclic, 93 convolutional, 56, 115, 187, 201, 399,449 Golay, 43 group, 297, 300 Kerdock, 391 negacyclic, 93 Nordstrom-Robinson, 391 Reed-Muller, 72, 149, 162,391 Reed-Solomon, 43, 74,83,141,209, 259 runlength-limited, 259 Ungerboeck, 74 Wyner-Ash, 264

code division multiple access, 357, 423 Codex Corporation, 115 coherent detection, 447 Cohn, D. L., 59 collision channel, 81, 353,419 collision entropy, 277 comma-free coding, 437 communication network, 13 complexity, 221 computational complexity, 223, 391

462

concatenation, 74, 109, 155, 162, 206, 259 conjugacy constraint, 44, 145 connection polynomial, 43 constacyclic code, 93 constant envelope signaling, 71 constraint length, 72, 73, 187 continuous-phase frequency shift keying, 333 convolution lemma, 143 convolution property, 141 convolutional code, 56, 115, 187, 201, 399,449 Coppersmith's algorithm, 223 Cooley-Tukey algorithm, 144 Costello, D. J., Jr., 69 covering radius, 450 Coxeter group, 297 crosstalk, 409 cryptanalyst, 97 cryptogram, 97 cryptography, 1, 96, 151, 180,221,227, 258, 271, 287 cryptology, 35 Csibi, S., 81 cutoff rate, 73, 315, 316, 454 cyclotomic set, 145

da Rocha, V. C., Jr., 93 data compression, 431 de Bruijn sequence, 39 defect, 193 demultiplexer, 263 Deng, R. H., 173 derivative, 228 DES, 227 Diaconis' problem, 26 differential, 231 differential cryptanalysis, 227 differential minimum-shift-keying, 333 Diffie-Hellman key exchange, 1 dihedral group, 298 discrete logarithm problem, 223 disk access time, 60

disk drive, 60 diversity modulation, 333 divide and conquer, 294 Doppler shift, 131 Drolet, G., 381 dual lattice, 124

Elias bound, 400 Elias, P., 101 elliptic curve, 7 encoding matrix, 187 entropy, 293, 411, 432 erasure channel, 84, 89 Ericson, T., 109 Erlang capacity, 423 error-correction, 263 error detection, 263 error locator, 451 Euclidean algorithm, 211 Euclidean norm, 123

fading, 423 fading channel, 130, 155, 235 Fano algorithm, 73 Fano's lemma, 274 fast algorithm, 209 feedback information, 353 feedback polynomial, 222 finite Fourier transform, 142 finite geometry, 101 finite reflection group, 297, 298 Forney, G. D., Jr., 115 Frechet space, 309 free Hamming distance, 399 frequency hopping, 81, 137

Galileo mission, 73 Gallager, R. G., 129 Galois field, 26 Gauss sum, 326 Gaussian channel, 236 Gaussian elimination, 213 generalized concatenated code, 394 generalized constraint length, 187 generator matrix, 189

463

Golay code, 43 Golay merit factor, 325 Gollmann, D., 35 Good-Thomas algorithm, 144 Gossett lattice, 123 gradient algorithm, 365 Green Machine, 72 group

Coxeter, 297 dihedral, 298 finite reflection, 297 isometry, 297

group code, 300 Gunther, C. G., 141 Gyorfi, L., 81

Hadamard transform, 391 Hagenauer, J., 155 Hamming bound, 251,258 Hamming distance, 236 Han-Kobayashi region, 411 Hankel map, 308 Hankel matrix, 214 Hankel matrix factorization, 209 Haroutunian, H. S., 13 hash function, 252, 258, 278 Hasse derivative, 94, 146 Heinrich Hertz Institut, 263 Heller bound, 400 Herro, M. A., 173 hexagonal lattice, 109 Hoeffding's inequality, 85

IDEA cipher, 227 Information Theory Transactions, 263 Ingemarsson, I., 179 insecure channel, 273 integral lattice, 124 INTELSAT, 72 interference channel, 409 interleaving, 155 International Symposium on Informa­tion Theory, 263 intraset distance, 237

invariant-factor theorem, 187 inverse filter, 357 inverse Fourier transform, 144, 150 invertible sequence, 323 Iwahori theorem, 298, 304

Jet Propulsion Laboratory, 73 Johannesson, R., 187 Justesen, J., 201

Kailath, T., 209 Kalman filter, 158,216 Kerdock code, 391 key equation, 210 Key's theorem, 149 Khachatrian, L. H., 13 Krawtchouk polynomial, 53 Kronecker indices, 375 Kuhn, G. J., 221

Lai, Xuejia, 227 Lanczos algorithm, 213 Lanczos recursions, 209 lattice, 123

dual, 124 Gosset, 123 integral, 124

leaf entropy, 350 Legendre sequence, 325, 327 Lempel-Ziv algorithm, 431 Levenshtein bound, 110 Levinson algorithm, 209, 215 Li, Yuan Xing, 173 likelihood ratio, 155 Lin, S., 235 linear complexity, 35, 43, 288, 290 linear complexity profile, 36 linear complexity property, 44 linear feedback shift register, 35, 43, 221,287 linear system, 367 linear system theory, 123 Loeliger, H. A., 251 log-likelihood ratio, 117, 156

464

Lucas' lemma, 142, 150

magnetic storage, 173 Markov cipher, 227 Massey, J. L., 343 Massey-Omura lock, 1 Massey-Omura multiplier, 3 Massey's theorem, 43 Matt, H. J., 263 Maurer, U. M., 271 maximum distance separable code, 95 maximum likelihood decoding, 72, 160, 316,334,391,450 maximum likelihood estimation, 324 Meier, W., 287 Milne-Thomson theorem, 147 minimal polynomial, 368 minimum distance, 236 minimum Hamming distance, 95 minimum-shift-keying, 333 Minkowski-Hlawka theorem, 259 Minty algorithm 116, 126 Mittelholzer, T., 297 Mitter, S. K., 307 module homomorphism, 308 module theory, 307 multiaccess coding theorem, 135 multiaccess communication, 49, 81, 129, 252,258,315,357,409 multilevel code, 75, 235, 394 multipath, 129, 135, 323, 357 multiplexer, 263 multiuser communication, 135,357,409 Murphy, S., 35

Nakagami distribution, 132 Narayan, P., 315 NASA,75 near-far resistance, 135 negacyclic code, 93 network, 423 noise enhancement factor, 358 nonlinear code, 76 Noordwijk, 263

Nordstrom-Robinson code, 391 normal basis, 1 NRZI, 174 Nyquist signaling, 70

observability, 307 Odenwalder bound, 400 Odlyzko, A. M., 323 offset quadrature PSK, 333 one-time pad, 272 optical communication, 315 optical fiber, 173 optical storage, 173

packet, 82 Pareto exponent, 456 Parseval theorem, 141, 146 partial realization theory, 307 Paterson, K., 35 path multiplicity, 239 Penzhorn, W. T., 221 Perez, L. C., 69 permutation modulation, 298 PES cipher, 227 phase-shift-keying, 71, 442 Pioneer, 73, 115 Piper, F., 35 plaintext attack, 97, 227 Plotkin bound, 400 point to point communication, 130 Poisson process, 82 power limited signaling, 71 precoding, 447 privacy amplification, 276 probablity of decoding failure, 204 processing gain, 358 product distance, 236 protocol, 13, 82, 273, 423 pseudorandom generator, 287 public channel, 273, 276 public-key cryptography, 1, 272

quadrature amplitude modulation, 71, 75 quadrature phase-shift-keying, 71

465

Qualcomm, 129

RAID system, 60 Rajpal, S., 235 rake receiver, 133 random-access, 353 random-coding bound, 251, 252, 256 rational transfer function, 188 Rayleigh channel, 163, 236 Rayleigh distribution, 132 reach ability, 307 Riccati equation, 216 Rician distribution, 132 Rieger bound, 263 Rimoldi, B., 333 ring code, 76 ring of integers, 439 ring of polynomials, 439 Rip Van Winkle cipher, 179 root system, 298 rooted tree, 345 rotational invariance, 76, 447 rotational latency, 60 Rueppel, R. A., 343 runlength, 174 runlength-limited code, 259 running digital sum, 174 Ruprecht, J., 357 Ruprecht merit factor, 324

Sain, M. K., 367 satellite communication, 71 scattering theory, 216 Schur algorithm, 209, 216 secrecy capacity, 271 secret key rate, 271, 275 Seguin, G., 381 sequence, 37

Barker, 326, 381 binary, 381 de Bruijn, 39 invertible, 323 Legendre, 325, 327

sequential decoding, 73, 115, 317, 449, 453 set-partitioning, 401 Shannon, C. E., 69 Shannon entropy, 277 Shannon limit, 155 Shannon packing, 252, 257 shrinking generator, 287 signal constellation, 237 signal set partitioning, 235, 237 signal-to-noise ratio, 70 simple root, 299 simplex conjecture, 319 simplex signal set, 302, 315, 318 Singleton bound, 95 Snyder, D. L., 315 soft decision, 72 soft decision decoding, 155, 239 soft output, 157 space communication, 71, 115 span, 116 spectral efficiency, 70 spectral zero, 44 sphere packing, 252, 257 spherical code, 109 spread-spectrum communication, 180, 315 squared Euclidean distance, 236 Stack algorithm, 453 Staffelbach, 0., 287 stereo audio signal, 270 Stevenson, R. 1., 59 stream cipher, 147,221,287 Sun, Feng-Wen, 391 symmetric group, 26 synchronization, 174, 180,263,423 syndrome, 202, 258, 264 systems theory, 307

telephone channel, 76 theorem

Blahut, 141, 149 Cayley-Hamilton, 368 Iwahori, 298,304

466

Key, 149 Lucas, 142 Massey, 43 Milne-Thomson, 147 Minkowski-Hlawka, 259 multiaccess CDMA, 135 Parseval, 141

threshold decoding, 72, 115, 160, 399 time division multiple access, 357 time hopping, 84 Toeplitz equation, 215 torsion module, 368 transmission-line theory, 216 tree code, 116 trellis, 123, 201, 399 trellis code, 74,235,399,439 turbo-code, 74 two-way channel, 409

Ungerboeck code, 74,446 Ungerboeck, G., 399 uniquely decodable, 51 unit memory convolutional code, 202

van der Meulen, E. C., 409 van Tilborg, H. C. A., 391 Varshamov-Gilbert bound, 54,204, 251, 255,450 Viterbi algorithm, 73, 116, 120, 124, 155,158,201,239,334,399,443,449 Viterbi, A. J., 423 Voronoi region, 392 Voyager, 74, 75

Wagner decoding, 394 Wan, Zhe-Xian, 187 Wedderburn numbers, 375 weight, 44 weight retaining property, 93 Wild, P., 35 wireless communication, 130 Wyner, A. D., 431 Wyner-Ash code, 264

Zech's logarithm, 222

zero-error capacity, 419 Zetterberg, L. H., 439 Zigangirov, K. Sh., 449 Zinoviev, V., 109 Ziv, J., 431

467

PUBLICATIONS BY

James L. Massey

I Books

*[1] J. L. Massey, Threshold Decoding. Cambridge, MA: M.LT. Press, 1963.

*Awarded 1963 Paper Award by the IEEE Group on Information Theory.

II Books: Chapters in Contributed Volumes

[1] J. L. Massey, "Information, Machines, and Men," in Philosophy and Cybernetics (Eds. F. J. Crosson and K. M. Sayre). Notre Dame, IN: Notre Dame Press, 1967, pp. 37-69.

[2] J. L. Massey, "Advances in Threshold Decoding," in Advances in Communication Systems, Vol. III (Ed. A. Ralarishnan). New York: Academic Press, 1968, pp. 91-115.

[3] J. L. Massey, "Applications of Automata Theory in Coding," in Applied Automata Theory (Ed. J. Tou). New York: Academic Press, 1968, pp. 125-146.

[4] J. 1. Massey, "Error Correcting Codes," in Encyclopaedia of Linguistics, Information, and Control (Ed. A. R. Meetham). London: Pergamon, 1969, pp. 173-176.

[5] J. L. Massey and O. N. Garcia, "Error-Correcting Codes in Computer Arithmetic," in Advances in Information Systems Science, VolA (Ed. J. Tou). New York: Plenum Press, 1972, pp. 273-326.

[6] J. 1. Massey, "Coding Theory," in Handbook of Applicable Mathematics, Vol.5, Com­binatorics and Geometry (Eds. W. Lederman and S. Vajda). Chichester and New York: Wiley, 1985, pp. 623-676.

III Articles in Conference Proceedings Published in Book Form

[1] J. 1. Massey, "Some Algebraic and distance Properties of Convolutional Codes," in Error Correcting Codes (Ed. H. B. Mann). New York: Wiley, 1968, pp. 89-109.

[2] J. 1. Massey, "Methods of Alleviation of Ionospheric Scintillation Effects on Digital Communications," in Communication Satellite Developments: Technology, Progress in Astronautics and Aeronautics,Vol. 42 (Ed. W. G. Schmidt and G. E. LaVean). Cambridge, MA: M.LT. Press, 1976, pp. 279-287.

469

[3] J. 1. Massey, "The Codeword and Syndrome Methods for Data Compression with Error-Correcting Codes," in New Directions in Signal Processing in Communication and Control, (Ed. J. K. Skwirzynski), NATO Advanced Study Institutes Series E12. Leyden, The Netherlands: Noordhoff, 1975, pp. 3-13.

[4] J.1. Massey, "Markov Information Sources," in New Directions in Signal Processing in Communication and Control, (Ed. J. K. Skwirzynski), NATO Advanced Study Institutes Series E25. Leyden, The Netherlands: Noordhoff, 1975, pp. 15-26.

[5] J. L. Massey, "Error Bounds for Tree Codes, Trellis Codes, and Convolutional Codes with Encoding and Decoding Procedures," in Coding and Complexity (Ed. G. Longo with Preface by J. 1. Massey), CISM Courses and Lectures No. 216. Wien and New York: Springer-Verlag, 1976, pp.1-57.

[6] J. L. Massey, "Joint Source and Channel Coding," in Communication Systems and Random Process Theory (Ed. J. K. Skwirzynski), NATO Advanced Studies Institutes Series E25. The Netherlands: Noordhoff, 1978, pp. 279-293.

[7] J. L. Massey, "Collision-Resolution Algorithms and Random-Access Communications," in Multi-User Communication Systems (Ed. G. Longo), CISM Courses and Lectures No. 265. Wi en and New York: Springer, 1981, pp. 73-137.

[8] P. Schoebi and J. 1. Massey, "Fast Authentication in a Trapdoor-Knapsack Public Key Cryptosystem," in Cryptography (Ed. T. Beth), Lecture Notes in Computer Science, No. 149. New York: Springer, 1983, pp. 289-294.

[9] J. L. Massey, "An Information-Theoretic Approach to Algorithms," in The Impact of Processing Techniques in Communications (Ed. J. K. Skwirynski), NATO Advanced Study Institutes Series E91. Dordrecht, The Netherlands: Nijhoff, 1985, pp. 3-20.

[10] J. L. Massey and R. A. Rueppel, "Linear Ciphers and Random Sequence Generators with Multiple Clocks," in Advances in Cryptology-Eurocrypt '84 (Eds T. Beth, N. Cot and 1. Ingemarsson), Lecture Notes in Computer Science, No. 209. Heidelberg and New York: Springer 1985, pp. 74-87.

*[11] J. 1. Massey, "Cryptography - A Selective Survey," in Digital Communications (Eds. E. Biglieri and G. Prati). Amersterdam: North-Holand, 1986, pp. 3-21.

*Reprinted as Invited Paper in Alta Frequenza, Vol. 55, No.1, pp. 4-11, Jan. - Feb. 1986.

[12] J. 1. Massey, U. M. Maurer and M.-Z. Wang, "Non-Expanding, Key-Minimal, Robustly Perfect, Linear and Bilinear Ciphers," in Advances in Cryptology - Eurocrypt '87 (Eds. D. Chaum and W. 1. Price), Lecture Notes in Computer Science, No. 304. Heidelberg and New York: Springer, 1988, pp. 237-247.

[13] J. 1. Massey, "Channel Models for Random-Access Systems," in Performance Limits in Communication Theory and Practice (Ed. J.K. Skwirzynski), NATO Advances

470

Studies Institutes Series E142. Dordrecht, The Netherlands: Kluwer Academic, 1988, pp. 391-402.

*[14] J. 1. Massey, "Some New Approaches to Random-Access Communications," in Per­formance' 87 (Eds. P.-J. Courtois and G. Latouche), Proc. 12th IFIP WG 7.3 Int. Symp. in Computer Performance Modelling. Amsterdam and New York: North Hol­land 1988, pp. 551-569.

*Reprinted in Multiple Access Communications: Foundations for Emerging Tech­nologies (Ed. N. Abramson). New York: IEEE Press, 1993, pp. 354-378.

[15] J.1. Massey and T. Schaub, "Linear Complexity in Coding Theory," in Coding Theory and Applications (Eds G. Cohen and Ph. Godlewski), Lecture Notes in Computer Science, No. 311. Heidelberg and New York: Springer, 1988, pp. 19-32.

[16] H. N. Jendal, Y. J. B. Kuhn and J. L. Massey, "An Information-Theoretic Approach to Homophonic Substitution," in Advances in Cryptology-Eurocrypt' 89 (Eds. J.-J. Quisquater and J. Vandewalle), Lecture Notes in Computer Science, No. 434. Heidel­berg and New York: Springer, 1990, pp. 382-394.

[17] U. M. Maurer and J. L. Massey, "Perfect Local Randomness in Pseudo-Random Se­quences," in Advances in Cryptology-Crypto'89 (Ed. G. Brassard), Lecture Notes in Computer Science, No. 435. Heidelberg and New York: Springer, 1990, pp. 100-112.

[18] J. L. Massey, "The Relevance of Information Theory to Modern Cryptography," in Communications, Control and Signal Processing (Ed. E. Arikan), Proc. of 1990 Bilkent Int. Conference. Amsterdam: Elsevier, 1990, pp. 176-182.

[19] X. Lai and J. L. Massey, "A Proposal for a New Block Encryption Standard," in Ad­vances in Cryptology- Eurocrypt'90 (Ed. LB. Damgard), Lecture Notes in Computer Science No. 473. Heidelberg and New York: Springer, 1991, pp. 389-404.

[20] X. Lai, J. 1. Massey and S. Murphy, "Markov Ciphers and Differential Cryptanaly­sis," in Advances in Cryptology-Eurocrypt'91 (Ed. D. W. Davies), Lecture Notes in Computer Science No. 547. Heidelberg and New York: Springer 1991, pp. 17-38. [A preliminary version with the same title by X. Lai and J. L. Massey appears in AGEN Communications, Nr. 53, pp. 25-29, June 1991.]

[21] J. 1. Massey, "Contemporary Cryptology: An Introduction," in Contemporary Cryptology­The Science of Information Integrity (Ed. G. J. Simmons). New York: IEEE Press, 1992, pp. 1-39.

[22] J. 1. Massey, "Deep-Space Communications and Coding: A Marriage Made in Heaven," in Advanced Methods for Satellite and Deep Space Communications (Ed. J. Hage­nauer), Lecture Notes in Control and Information Sciences No. 182. Heidelberg and New York: Springer 1992, pp. 1-17.

471

[23] X. Lai and J. L. Massey, "Hash Functions Based on Block Ciphers," in Advances in Cryptology-Eurocrypt'92. (Ed. R. A. Rueppel), Lecture Notes in Computer Science, No. 658. Heidelberg and New York: Springer, 1993, pp. 55-70.

[24] J. L. Massey and T. Mittelholzer, "Welch's Bound and Sequence Sets for Code-Divison Multiple-Access Systems," in Sequences II: Methods in Communication, Security and Computer Sciences (Eds. R. Capocelli, A. De Santis and U. Vaccaro). Heidelberg and New York: Springer, 1993, pp. 63-78.

[25] C. P. Waldvogel and J. 1. Massey, "The Probability Distribution of the Diffie-Hellman Key," in Advances in Cryptology-Auscrypt'92 (Eds. J. Seberry and Y. Zheng), Lecture Notes in Computer Science No. 718. Heidelberg and New York: Springer 1993, pp. 492-504.

[26] V. C. da Rocha and J. 1. Massey, "A New Approach to the Design of Codes for the Binary Adder Channel," in Cryptography and Coding III (Ed. M. J. Ganley), IMA Conf. Series, New Series No. 45. Oxford: Clarendon Press, 1993, pp. 179-185.

[27] B. Blakley, G. R. Blakley, A. H. Chan and J. L. Massey, "Threshold Schemes with Disenrollment," in Advances in Cryptology Crypto'92 (Ed. E. F. Brickell), Lecture Notes in Computer Science No. 740. New York: Springer, 1993, pp. 540-548.

[28] J. 1. Massey, "SAFER K-64: A Byte-Oriented Block-Ciphering Algorithm," to appear in Proc. Cambridge Algorithms Workshop, Cambridge, England, 1994.

IV Articles in Refereed Journals

[1] W. W. Peterson and J. L. Massey, "Coding Theory," IEEE Trans. on Info. Theory, Vol. IT-9, pp. 223-229, Oct. 1963.

[2] J. L. Massey and R. Liu, "Application of Lyapunov's Direct Method to the Error­Propagation Problem in Convolutional Codes," IEEE Trans. on Info. Theory, Vol. IT-10, pp. 248-250, July 1964.

[3] J. L. Massey, "Reversible Codes," Information & Control, Vol. 7, pp. 369-380, Sept. 1964.

[4] J. L. Massey and R. Liu, "Equivalence of Nonlinear-Feedback Shift-Registers," IEEE Trans. on Info. Theory, Vol. IT-10, pp. 378-379, Oct. 1964.

[5] J. 1. Massey, "Survey of Residue Coding for Arithmetic Errors," ICC Bulletin, Vol. 3, pp. 195-209, Oct. 1964.

[6] J. L. Massey, "Implementation of Burst-Correcting Convolutional Codes," IEEE Trans. on Info. Theory, Vol. IT-ll, pp. 416-422, July 1965.

[7] J. 1. Massey, "Step-by-step Decoding of the Bose-Chaudhuri-Hocquenghen Codes," IEEE Trans. on Info. Th., Vol. IT-ll, pp. 580-585, Oct. 1965.

472

[8] J. L. Massey, "Uniform Codes," IEEE Trans. on Info. Th., Vol. IT-12, pp. 132-134, April 1966.

[9] J. L. Massey, "Note on Finite-Memory Sequential Machines," IEEE Trans. on Elec. Comp., Vol. EC-15, pp. 658-659, Aug. 1966.

[10] J. L. Massey and L. V. Auth, "Impedance Magnitude Measurements from a Resistive Bridge," IEEE Trans. on Education, Vol. E-10, pp. 50-51, March 1967.

*[11] J. L. Massey, "Shift-Register Synthesis and BCH Decoding," IEEE Trans. on Info. Th., Vol. IT-15, pp. 122-127, Jan. 1969.

*Reprinted in Algebraic Coding Theory: History and Development

(Ed. 1. F. Blake), Benchmark Papers in Electrical Engineering and Computer Science. Stroudsburg, PA: Dowden, Hutchison and Ross, 1973, pp. 233-238.

[12] J. L. Massey and M. K. Sain, "Codes, Automata and Continuous Systems: Explicit Interconnections, " IEEE Trans. on Auto. Control, Vol.AC-12, pp. 644-50, December 1967. [Also appears in Proc. NEC, Vol. 23, pp. 33-38, 1967.]

**[13] J. L. Massey and M. K. Sain, "Inverses of Linear Sequential Circuits," IEEE Trans. on Computers, Vol. C-17, pp. 330-337, April 1968. [See also J. 1. Massey and M. K. Sain, "Postscript to Inverses of Linear Sequential Circuits," IEEE Trans. on Comput­ers, Vol. C-17, pp.1177, Dec. 1968.]

** Reprinted in Key Papers in the Development of Coding Theory (Ed. E. R. Berlekamp). New York: IEEE Press, 1974, pp. 205-212.

[14] M. K. Sain and J. L. Massey, "Invertibility of Linear, Time-Invariant Dynamical Systems," IEEE Trans. on Auto. Cont.,Vol. AC-14, pp. 141-149, April 1969.

[15] J. L. Massey, "Variable-Length Codes and the Fano Metric," IEEE Trans. on Info. Th., Vol. IT-18, pp. 196-198, Jan. 1972.

[16] J. L. Massey and D. J. Costello, Jr., "Nonsystematic Convolutional Codes for Se­quential Decoding in Space Applications," IEEE Trans. Com. Tech., Vol. Com-19, pp. 806-813, Oct. 1971.

[17] J. L. Massey, "Optimum Frame Synchronization," IEEE Trans. on Comm., Vol. COM-20, pp. 115-119, April 1972.

[18] J. L. Massey, M. K. Sain and J. M. Geist, "Certain Infinite Markov Chains and Sequential Decoding," Discrete Math., Vol. 3, pp. 163-175, Sept. 1972.

[19] J. L. Massey, D. J. Costello, Jr., and J. Justesen, "Polynomial Weights and Code Constructions," IEEE Trans. Info. Th., Vol. IT-19, pp. 101-110, Jan. 1973.

[20] J. L. Massey, "On the Fractional Weight of Distinct Binary n-Tuples," IEEE Trans Info.Th., Vol. IT-20, pp. 131, Jan. 1974

473

[21] R. J. Matt and J. L. Massey, "Determining the Burst-Correcting Limit of Cyclic Codes," IEEE Trans. Info. Th., Vol. IT-26, pp. 289-297, May 1980.

[22] J. 1. Massey, "Capacity, Cut-Off Rate, and Coding for a Direct-Detection Optical Channel," IEEE Trans. Comm., Vol Com-29, pp. 1615-1612, Nov. 1981.

[23] J. 1. Massey, "What is a Bit of Information?," Scientia Electrica, Vol. 28, No.1, pp. 1-11,1982. Reprinted in German Translation as "Was ist ein Bit Information?," Frequenz, Band 37, S. 110-115, Mai 1983.

[24] M. Schlatter and J. L. Massey, "Capacity of Interconnected Ring Communication systems with Unique Loop-free Routing," IEEE Trans. on Info. Th., Vol. IT-29, pp. 774-778, Sept. 1983.

*[25] J. L. Massey and P. Mathys, "The Collision Channel without Feedback,", IEEE Trans. Info. Th., Vol. IT-31, pp. 192-204, March 1985.

*Awarded the IEEE 1986 W. R. G. Baker Award.

[26] J. 1. Massey, "Standardisierung Kryptographischer Dienste," Bulletin des Schweiz­erischen Elektrotechnischen Vereins, Vol. 77, No.7, pp. 367-372, 12 April 1986.

[27] Z. Zhang, T. Berger and J. 1. Massey, "Some Families of Zero-Error Block Codes for the 2-User Binary Adder Channel with Feedback," IEEE Trans Info. Th., Vol. IT-33, pp. 613-619, Sept. 1987.

[28] J. 1. Massey, "Probabilistic Encipherment," E. & M. (Elektrotechnik & Maschinen­bau, Austria), Vol. 104, No. 12, pp. 561-562, Dec. 1987.

[29] J. L. Massey, "An Introduction to Contemporary Cryptology," Proc. IEEE, Vol 76, pp. 533-549, May 1988.

[30] W. Rirt and J. L. Massey, "Capacity of the Discrete-Time Gaussian Channel with Intersymbol Interference," IEEE Trans. Info. Th., Vol. IT-34, pp. 380-388, May 1988.

[31] G. Z. Xiao and J. L. Massey, "A Spectral Chracterization of Correlation-Immune Combining Functions," IEEE Trans. Info. Th., Vol. IT-34, pp. 569-571, May 1988.

[32] U. M. Maurer and J. L. Massey, "Local Randomness in Pseudorandom Sequences," J. of Cryptology, Vol. 4, No.2, pp. 135-149, 1991.

[33] G. Gastagnoli, J. L. Massey, P. Schoeller and N. von Seeman, "On Repeated-Root Cyclic Codes," IEEE Trans. Info. Th., Vol. IT-37, pp. 337-342, March 1991.

[34] U. M. Maurer and J. L. Massey, "Cascade Ciphers: The Importance of Being First," J. of Cryptology, Vol. 6, No.1, pp. 55-61, 1993

[35] N. Q. A, 1. Gyorfi and J. L. Massey, "Constructions of Binary Constant-Weight Cyclic Codes and Cyclically Permutable Codes," IEEE Trans. Info. Th., Vol. IT-38, pp. 940-949, May 1992.

·474

[36] J. L. Massey, "Linear Codes with Complementary Duals," Discrete Math., Vol. 106/107, pp. 337-342, 1992. [Also appears in A Collection of Contributions in Honor of Jack van Lint (Eds. P. J. Cameron and H. C. A. van Tilborg), Topics in Discrete Math. 7. Amsterdam: Elsevier 1992, pp. 337-342.]

[37] F. D. Neeser and J. 1. Massey, "Proper Complex Random Processes with Applications to Information Theory," IEEE Trans. Info. Th., Vol. IT-39, pp. 1293-1302, July 1993.

[38] M. Rupf and J. 1. Massey, "Optimum Sequence Multisets for Synchronous Code­Division Multiple-Access Channels," to appear in IEEE Trans. Info. Th., 1994.

[39] X. Yang and J. 1. Massey, "The Condition for a Cyclic Code to Have a Complementary Dual," to appear in Discrete Math., 1994.

[40] M. Rupf , F. Tarkoy and J. 1. Massey, "User-Separating Demodulation for Code­Division Multiple-Access Systems," to appear in IEEE J. Selected Areasin Comm., 1994.

[41] D. R. Stinson and J. 1. Massey, "An Infinite Class of Counterexamples to a Conjecture Concerning Non-Linear Resilient Functions," to appear in J. of Cryptology, 1994.

V Articles in Conference Proceedings and Non-Refereed Journals

*[1] J. L. Massey, "Error-Correcting Codes Applied to Computer Technology," in Proc. Nat. Elec. Coni., Vol. 19, Oct. 1963, pp. 142-147.

*Awarded the Best Tutorial Paper Award at the 1963 National Electronics Confer­ence.

[2] J. 1. Massey and R. Liu, "Monotone Feedback Shift-Registers," in Proc. of 2nd Annual Allerton Conference on Circuit & System Theory, 1964, pp. 864-874.

[3] J. 1. Massey and R. Liu, "A New Diagram for Feedbck Shift-Registers," in Proc. of 3rd Annual Allerton Coni. on Circuit & Systems Theory, 1965 pp. 73-81.

[4] J. L. Massey and M. K. Sain, "Inverse Problems in Coding, Automata and Continuous Systems," in IEEE Coni. Record of 8th Symposium on Switching and Automata Theory, Oct. 1967, pp. 226-232.

[5] J. 1. Massey, "Catastrophic Error-Propagation in Convolutional Codes," in Proc. 11th Midwest Circuit Th. Symp., 1968, pp. 583-587.

[6] J. 1. Massey and M. K. Sain, "Trunk and Tree Searching Properties of the Fano Sequential Decoding Algorithm," in Proc. of 6th Annual Allerton Coni. on Circuit and System Theory, 1968, pp. 153-160.

[7] J. 1. Massey and M. K. Sain, "A Modified Inverse for Linear Dynamical Systems," in Proc. IEEE 8th Adaptive Processes Symp., 1969, pp. 5al-5a3.

475

[8] J. L. Massey and M. K. Sain, "Derivative Controllability," in Proc. 4th Princeton Conf. on Info. Sci. and Systems, 1970, p. 189.

[9] J. L. Massey, "Can Coding Beat the System?," in IEEE Int. Convention Digest, 1970, pp. 354-355.

[10] J. J. Uhran, Jr., and J. 1. Massey, "Analysis of Satellite Communications in a Multi­path Environment," in ICC '70 Conf. Record, 1970, pp. 10-20 to 10-24.

[11] J. L. Massey, "Coding and Modulation in Digital Communications," in Proc. Int. Zurich Seminar on Digital Comm., 1974, pp. E2(1)-E2(4).

[12] J. L. Massey and J. J. Uhran, Jr., "Sub-Baud Coding," in Proc. 13th Annual Allerton Conf. on Circuit and System Theory, 1975, pp. 539-547.

[13] J. L. Massey, "The Statistical Significance of Error Probability as Determined from Decoding Simulations for Long Codes," in Proc. 7th Annual Pittsburgh Conf. on Modeling and Simulation, April 26-27, 1976, pp. 63-64.

[14] J. L. Massey, "The Use of Redundant Packets in Slotted Aloha Type Random Access Schemes," in Proc. 1978 Conf. on Info. Sciences and Systems, March 29-31, 1978, pp. 78-81.

[15] J. L. Massey, "Foundations and Methods of Channel Encoding," in Proc. Int. Conf. on Info. and System Theory in Digital Comm., NTG-Fachberichte, Band 65, 1978, pp. 148-157.

[16] J. L. Massey, "Coding Techniques for Digital Data Networks," in Proc. Int. Conf. on Info. and System Theory in Digital Comm., NTG-Fachberichte, Band 65, 1978, pp. 307-315.

[17] J. 1. Massey, "A Generalized Formulation of Minimum Shift Keying Modulation," in ICC '80 Conf. Record, Vol. 2, 1980, pp. 26.5.1-26.5.4.

[18] J. L. Massey, "Logarithms in Finite Cyclic Groups-Cryptographic Issues," in Proc. 4th Benelux Symp. on Info. Theory, 1983, pp. 17-25.

[19] J. 1. Massey, "A Simplified Treatment of Wyner's Wire-Tap Channel," in Proc. 21st Allerton Conf. on Comm., Control and Computing, 1983, pp. 268-276.

[20] J.1. Massey, A. Gubser, A. Fischer and P. Hochstrasser, B. Huber and R. Sutter, "A Self-Synchronizing Digital Scrambler for Cryptographic Protection of Data," in Proc. Int. Zurich Seminar on Digital Comm., 1984, pp. 163-169.

[21] J. L. Massey, "The How and Why of Channel Coding," in Proc. Int. Zurich Seminar on Digital Comm., 1984, pp. 67-73.

*[22] J. L. Massey, "Information Theory, The Copernician System of Communications," Proc. ICC '84, Vol. 1, 1984, pp. 159-162.

*Reprinted in IEEE Communication Magazine, Vol. 22, pp. 26-28, Dec. 1984.

476

[23] J. L. Massey, "Delayed-Decimation/Square Sequences," Proc. 2nd Joint Swedish­Soviet Int. Workshop on Info. Th., 1985, pp. 118-123.

[24] Z. Zhang, T. Berger and J. L. Massey, "Some Families of Zero-Error Codes for the 2-User Binary Adder Channel," in Proc. 23rd Allerton Con£. on Comm., Control and Computing, 1985.

**[25] A. S. Glass and J. L. Massey, "Plastic Cards- How Smart is Secure?," Landis & Gyr Review, Vol 32, No.2, pp. 22-38, 1986.

**Reprinted in German version, "Plastikkarten - wie intelligent ist sicher? ," in Schweiz­erische Technische Zeitschrift, No.9, pp. 10-20, No. 10, pp. 36-46, and No. 11, pp. 21-29, May-June, 1986.

[26] J. 1. Massey, "Cryptography and System Theory," in Proc. 24th Allerton Con£. on Comm., Control and Computing, 1986, pp. 1-8.

[27] J. L. Massey, "On the Entropy of Integer-Valued Random Variables," in Proc. 1988 Beijing Int. Workshop on Info. Th., 1988, pp. C1.1-C1.4,.

[28] X. Lai and J. L. Massey, "Some Connections between Scramblers and Invertible Au­tomata," in Proc. 1988 Beijing Int. Workshop on Info. Th., 1988, pp. DI5.1-DI5.5.

[29] J. L. Massey, "A Short Introduction to Coding Theory and Practice," in Proc. Int. Symp. on Signals, Systems and Electronics, 1989, pp. 629-633.

[30] J. L. Massey and T. Mittelholzer, "Convolutional Codes over Rings," in Proc. 4th Joint Swedish-Soviet Int. Workshop on Info. Th., 1989, pp. 14-18.

[31] J. 1. Massey and T. Mittelholzer, "Systematicity and Rotational Invariance of Con­volutional Codes over Rings," in Proc. 2nd Int. Workshop on Algebraic and Combi­natorial Coding Theory, Leningrad, 1990, pp. 154-158.

[32] J. L. Massey, "Causality, Feedback and Directed Information," in Proc. 1990 Int. Symp. on Info. Th. & its Applications, 1990, pp. 303-305.

[33] R. A. Rueppel and J. L. Massey, "The Security of N atel D GSM" [presented at the Berner Technologie Forum on Mobile Communications, Berne, Oct. 24, 1991] Technische Mitteilungen PTT, No.3, pp. 108-112, 1992. (Republished in German as "Die Sicherheit von Natel D GSM," Technische Mitteilungen PTT, No.4, pp. 150-153, 1992. )

[34] J. L. Massey, "Coding and Modulation for Code-Division Multiple Accessing," in Proc. Third Int. Workshop on Digital Signal Processing Techniques Applied to Space Communications, ESTEC, Noordwijk, 1992, pp. 3.1-3.17.

[35] J. L. Massey, "Some Applications of Source Coding in Cryptography," in Proc. 3rd Symp. on State and Progress of Research in Cryptography, Rome, 1993, pp. 143-160.

[36] J. L. Massey, "Minimal Codewords and Secret Sharing," in Proc. 6th Joint Swedish­Russian Int. Workshop on Info. Theory, 1993, pp. 276-279.

477

VI Papers Presented at IEEE International Symposia on Information Theory

[1] J. 1. Massey, "Uniform Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1966, p. 19.

[2] J. L. Massey and M. K. Sain, "Distribution of the Minimum Cumulative Metric for Sequential Decoding," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1969, p. 56.

[3] J. L. Massey and J. J. Uhran, Jr., "Sub-Baud Coding and Cyclic Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1970, pp. 25-26.

[4] D. J. Costello, Jr., and J. 1. Massey, "Constructing Good Convolutional Codes from Cyclic Block Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1972, p. 44.

[5] J. L. Massey, "An Error Bound for Random Tree Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1973, pp. D3.1-D3.2.

[6] J. L. Massey, "An Information-Theoretic Approach to Data-Processing Algorithms," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1974, pp. 35-36.

[7] J. L. Massey, "All Signal Sets Centered about the Origin Are Optimal at Low Energy­to-Noise Ratios on the AWGN Channel," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1976, pp. 80-81.

[8] J. 1. Massey, "A Class of Maximum Distance Separable Codes over GF(p) Encodable Using Only Addition and Subtraction," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1976, p. 133.

[9] J. L. Massey, "Shannon's 'Proof' of the Noisy Coding Theorem," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1977, p. 107.

[10] J. 1. Massey, "Convolutional Codes - Theory Lagging Practice," in Abstracts of Pa­pers, IEEE Int. Symp. on Info. Tb., 1979, p. 20.

[11] J. 1. Massey, "Capacity, Cut-Off Rate, and Coding for a Direct-Detection Optical Channel," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1981, p. 58.

[12] J. L. Massey, "Effect of Channel Error on the Capetanakis and Related Random­Access Algorithms," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1981, p. 65.

[13] M. Schlatter and J. L. Massey, "Capacity of Interconnected Ring Communication Systems with Unique Loop-Free Routing," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1982,p. 61-62.

[14] J.1. Massey, "The Capacity of the Collision Channel without Feedback," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1982, p. 101.

478

[15] J. L. Massey, "The Entropy of a Rooted Tree with Probabilities," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1983, p. 127.

[16] N. Q. A, L. Gyorfi, and J. L. Massey, "Some Constructions of Protocol Sequences for Collision Channels and a Class of Optimum Cyclic Constant Weight Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1985, p. 40.

[17] R. A. Rueppel and J. 1. Massey, "The Knapsack as a Nonlinear Function," in Ab­stracts of Papers, IEEE Int. Symp. on Info. Th., 1985, p. 46.

[18] I. Ingemarsson and J. L. Massey, "Synchronization of Truly Random Binary Se­quences," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1985, p. 57.

[19] D. J. Costello, Jr., and J. L. Massey, "A Lower Bound on the Minimum Distance Growth Rate of Fixed Convoutional Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1985, p. 90.

[20] W. Hirt and J. 1. Massey, "On the Mutual Information and Cut-Off Rate of Channels with Intersymbol Interference," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1985, pp. 114-115.

[21] J. L. Massey and I. Ingamarsson, "The Rip van Winkle Cipher - A Simple and Prov­ably Computionally Secure Cipher with a Finite Key," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1985, p. 146.

[22] J. 1. Massey, N. von Seeman and P. Schoeller, "Hasse Derivatives and Repeated-Root Cyclic Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1986, p. 39.

[23] T. Schaub and J. L. Massey, "Bounds on the Minimum Distance of Cyclic Codes via Bounds on the Linear Complexity of Periodic Sequences with Known Patterns of Zeros," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1986, p. 71.

[24] A. Gubser and J. L. Massey, "Node Synchronization of R = 1/2 Binary Convolutional Codes," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1986, p. 127.

[25] N. Q. A, L. Gyorfi, and J. L. Massey, "Families of Sequences with Optimal Generalized Hamming Correlation Properties," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1986, pp. 136-137.

*[26] J. 1. Massey, "Towards a Proof of the Simplex Conjecture?," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1988, p. 59.

*Presented as the Shannon Lecture at this symposium.

[27] J. Ruprecht and J. L. Massey, "Binary Input Sequences for Maximum-Likelihood Estimation of Multipath Channels," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1990, p. 32.

[28] U. M. Maurer and J. L. Massey, "Cascade Ciphers: The Importance of Being First," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1990, p. 118.

479

[29] J. 1. Massey, T. Mittelholzer, T. Riedel and M. Vollenweider, "Ring Convolutional Codes for Phase Modulation," in Abstracts of Papers, IEEE Int. Symp. on Info. Th., 1990, p. 176.

[30] J. L. Massey, "On Welch's Bound for the Correlation of a Sequence Set," in Proc. IEEE Int. Symp. on Info. Th., 1991, p. 385.

[31] B. Blakley, G. R. Blakley, A. H. Chan and J. L. Massey, "Threshold Schemes with Disenrollment," in Proc. IEEE Int. Symp. on Info. Th., 1993, p. 229.

[32] M. Rupf and J. L. Massey, "Optimum Sequence Multisets for Symbol-Synchronous Code-Division Multiple-Access Channels," in Proc. IEEE Int. Symp. on Info. Th., 1993, p. 373.

[33] J. 1. Massey, "Guessing and Exponentiated Entropy," to appear in Proc. IEEE Int. Symp. on Info. Th., 1994.

VII Published Book Reviews

[1] J. L. Massey, (Information Theory by R. Ash. New York: Wiley, 1965) IEEE Trans. Info. Th., Vol. IT-12, pp. 488-489, Oct. 1966.

[2] J.1. Massey, (An Introduction to Error-Correcting Codes by S. Lin. Englewood Cliffs, N. J.: Prentice-Hall, 1970) IEEE Trans. Info. Th., Vol. IT-17, pp. 768-769, Nov. 1971.

[3] J. L. Massey, (Topics in Mathematical System Theory by R. E. Kalman, P. 1. Falb, and M. A. Arbib, Part III; Automata Theory. New York: McGraw-Hill, 1969) IEEE Trans. Auto. Cont., Vol. AC-17, p. 182, Feb. 1972.

[4] J. L. Massey, (Error-Correcting Codes, 2nd Edition, by W. W. Peterson and E. J. Weldon, Jr., Cambridge, Mass. and London, M.I.T. Press, 1972) IEEE Trans. Info. Th., vol IT-19, pp. 373-374, May 1973.

[5] J. L. Massey, (The Theory of Error-Correcting Codes by F. J. MacWilliams and N. J. A. Sloane. Amsterdam: North-Holland and New York: Elsevier/North Holland, 1977) IEEE Trans. Info. Th.,Vol. IT-15, pp. 501-502, July, 1979.

[6] J.1. Massey, (Theory and Practice of Error Control Codes by R. E. Blahut. Reading, MA: Addison-Wesley, 1983) IEEE Trans. Info. Th. , Vol. IT-31, pp. 553-554, July 1985. Reprinted in Proc. IEEE, Vol. 74, pp. 1293-1294,1986.

VIII U. S. Patents

[1] J. L. Massey, U. S. Patent No. 3,303,333, "Error Detection and Correction System for Convolutional Codes," Feb. 7, 1967.

[2] J. 1. Massey, U. S. Patent No. 3,402,393, "Error Detection and Correction in Signal Transmission by Use of Convolutional Codes," Sept. 17, 1968.

480

[3] J.1. Massey, U. S. Patent No. 3,439,334, "Processing Signal Information," April 15, 1969.

[4] J. L. Massey, U. S. Patent No. 3,500,320, "Error Correcting Means for Digital Trans­mission Systems," March 10, 1970.

[5] J. L. Massey, U. S. Patent No. 3,566,352, "Error Correction in Coded Messages," Feb. 23, 1971.

[6] J. L. Massey and T. Schaub, U. S. Patent No. 4,506,372, "Method and Apparatus for Recognizing in a Receiver the Start of a Telegram Signal Consisting of a Bit Impulse Sequence," March 19, 1985.

[7) J. L. Massey and J. K. Omura, U. S. Patent No. 4,567,600, "Method and Apparatus for Maintaining the Privacy of Digital Messages Conveyed by Public Means," Jan. 28, 1986.

[8] J. K. Omura and J. 1. Massey, U. S. Patent No. 4,587,627, "Computational Method and Apparatus for Finite Field Arithmetic," May 6, 1986.

[9] J. L. Massey and R. A. Rueppel, U. S. Patent No. 4,797,922, "Method of, and Ap­paratus for, Transforming a Digital Data Sequence into an Encoded From," Jan. 10. 1989.

[10] J. 1. Massey, U. S. Patent No. 5,170,412, "Multiple Access Method," Dec. 8, 1992.

[11] J. L. Massey and X. Lai, U. S. Patent No. 5,214,703, "Device for the Conversion of a Digital Block and Use of Same," May 25, 1993.

481