Articles

 

Coding: Journal Articles, Conference Proceedings, and Technical Reports

Berlekamp, E.R., 2002, "The Performance of Block Codes", Notices of the AMS, January 2002, 17-22.

Berlekamp, E.R., R. Hill, and J. Karim, 1998, "The solution of a problem of Ulam on searching with lies" Proceedings of the IEEE International Symposium on Information Theory, August 16-21, 1998. pages 244-247. DOI 10.1109/ISIT.1998.708849

Berlekamp, E.R., 1996, "Bounded Distance+1 Soft-Decision Reed-Solomon Decoding", IEEE Trans. Inform. Theory, IT 42: 704-720. Corrected version

Berlekamp, E.R., G. Seroussi, and P. Tong, 1994, "A Hypersystolic Reed-Solomon Decoder", Reed-Solomon Codes and Their Applications, S.B. Wicker and V.K. Bhargava (eds.), New York: IEEE Press

Berlekamp, E.R., and P.T. Liu, 1989, "Elongated Burst Correction With Reed-Solomon Codes", Proceedings of the International Conference on Communication Technology, Beijing, China, July 1989.

Berlekamp, E.R., Peile, R.E., Pope, S.P., 1987, "The Application of Error Control To Communications", IEEE Communications Magazine, Vol. 25, No. 4

Berlekamp, E.R., 1986, "Variable Depth Helical Interleavers", Cyclotomics technical report to NSF.

Berlekamp, E.R., R.J.Currie, R.J. McEliece, C.K. Rushforth, and P. Tong, 1986, "An Error-Control Code With An Imbalance Of Ones And Zeros To Provide A Residual Carrier Component", IEEE MILCOM Conference, October 5, 1986.

Berlekamp, E.R., William E. Toms, and Jerry Shifman, 1986, "An Application Of Reed-Solomon Codes To A Satellite TDMA System", IEEE MILCOM Conference.

Berlekamp, E.R., 1983, "The Construction Of Fast High-Rate Soft-Decision Block Decoders", IEEE Trans. Inform. Theory, IT 29: 372-377.

Berlekamp, E.R., 1982, "Bit-Serial Reed-Solomon Encoders", IEEE Trans. Inform. Theory, IT 28:869-874.

Berlekamp, E.R., and McEliece, Robert J., l982, "Average Case Optimized Buffered Decoders", Cyclotomics, Inc., Berkeley, CA.

Berlekamp, E.R., 1982, "Error-Correcting Codes For Digital Audio", Collected Papers From The Audio Engineering Society Premiere Conference.

Berlekamp, E.R., 1980, "The Technology Of Error-Correcting Codes", Proc.of the IEEE, 68: 564-593.

Berlekamp, E.R., and J.L. Ramsey, 1978, "Readable Erasures Improve The Performance Of Reed-Solomon Codes (Corresp.)", IEEE Trans. Inform. Theory, IT 24:632-633.

Berlekamp, E.R., R.J. McEliece, and H.C.A. Van Tilborg, 1978, "On The Inherent Intractability Of Certain Coding Problems", IEEE Trans. Inform. Theory, IT 24:384-386.

Berlekamp, E.R., 1977, "Long Block Codes Which Use Soft Decisions And Correct Erasure Bursts Without Interleaving", pp. 1-2 in Proc. of the National Telecommunications Conference, Los Angeles.

Berlekamp, E.R., 1975, "Algebraic Codes For Improving The Reliability Of Tape Storage", pp.497-499 in Proceedings of the AFIPS Conference.

Berlekamp, E.R., and J. Justesen, 1974, "Some Long Cyclic Linear Binary Codes Are Not So Bad", IEEE Trans. Inform. Theory, IT 20:351-356.

Berlekamp, E.R., and 0. Moreno, 1973, "Extended Double-Error Correcting Binary Goppa Codes Are Cyclic", IEEE Trans. Inform. Theory, IT 19:817-818.

Berlekamp, E.R., 1973, "Goppa Codes", IEEE Trans. Inform. Theory, IT 19:590-592.

Berlekamp, E.R., 1973, "The Golay-Viterbi Concatenation Scheme", JPL Technical Report 32-1526, Vol. 16.

Kerdock, A.M., ghost written and communicated by Berlekamp, E.R., 1972, "A Class Of Low-Rate Nonlinear Binary Codes", Information and Control, Vol. 20, No. 2.

Berlekamp, E.R., 1972, "A Survey Of Coding Theory", J. Royal Stat. Soc. Series A, 135:44-73.

Berlekamp, E.R., 1972, "Long Primitive Binary BCH Codes Have Distance d-2n ln R^-l/log n...", IEEE Trans. Inform. Theory, IT 18:415-426.

Berlekamp, E.R., F.J. MacWilliams, and N.J.A. Sloane, 1972, "Gleason's Theorem On Self-Dual Codes", IEEE Trans Inform. Theory, IT 18:409-414.

Berlekamp, E.R., and L.R. Welch, 1972, "Weight Distributions Of the Cosets Of The (32,6) Reed-Muller Code", IEEE Trans. Inform. Theory, IT 18:203-207.

Berlekamp, E.R., 1971, "Coding Theory And The Mathieu Groups", Inform. Control, 18:40-64.

Berlekamp, E.R., and N.J.A. Sloane, 1970 "Weight Enumerator For Second-Order Reed-Muller Codes", IEEE Transactions on Information Theory, Vol. IT-16, No. 6.

Berlekamp, E.R., 1970, "The Weight Enumerators For Certain Subcodes Of The Second Order Binary Reed-Muller Codes", Inform. Control, 17:485-500

Berlekamp, E.R., 1970, "Doubly Extended RS Codes Are Cyclic After Prenormalization". Tech. Memo, Bell Telephone Laboratories.

Berlekamp, E.R., and N.J.A. Sloane, 1969, "Restrictions On Weight Distribution and Reed-Muller Codes", Inform. Control, 14:442-456; Math. Rev., 39:5215

Berlekamp, E.R., 1969, "A Survey Of Coding Theory", pp. 3-11 in Proceedings of the Waterloo Conference on Combinatorial Mathematics, RECENT PROGRESS IN COMBINATORICS, Academic Press, Inc., New York.

Berlekamp, E.R., 1969, "Techniques For Computing Weight Enumerators", Tech Memo, Bell Telephone Laboratories

 

Berlekamp, E.R., 1969, "On The Carlitz-Uchiyama Bound", Tech. Memo, Bell Telephone Laboratories.

 

Berlekamp, E.R., 1968, "Nonbinary BCH Decoding", IEEE Trans. Inform.Theory, IT 14:242.

Berlekamp, E.R., 1968, "Block Coding For The Binary Symmetric Channel With Noiseless, Delayless Feedback", pp. 61-88 in H.B. Mann (ed.), ERROR-CORRECTING CODES, Wiley & Sons, New York.

Berlekamp, E.R., 1968, "Weight Enumeration Theorems", pp. 161-170 in Proc. 6th Annual Allerton Conf. Circuit and Systems Theory, Univ. Illinois Press, Urbana, Illinois.

Berlekamp, E.R., 1967, "Negacyclic Codes For The Lee Metric", in COMBINATORIAL MATHEMATICS AND ITS APPLICATIONS, R.C. Bose, and T.A. Dowling (eds.), University of North Carolina Press, Chapel Hill, North Carolina.

Golomb, S.W., Berlekamp, E.R., Cover, T.M., Gallager, R.G., Massey, J.L., and Viterbi, A.J., 2002 "Claude Elwood Shannon (1916-2001)", Notices of the AMS, January 2002, 8-16.

Jacobs I.M. and E.R. Berlekamp 1967, "A Lower Bound To The Distribution Of Computation For Sequential Decoding", IEEE Transactions on Information Theory, Vol. IT-13, No. 2, pp 167-174.

Shannon, C.E., R.G.Gallager, and E.R. Berlekamp, 1967, "Lower Bounds To Error Probability For Coding On Discrete Memoryless Channels II", Inform. Control, 10:522-552.

Shannon, C.E., R.G.Gallager, and E.R. Berlekamp, 1967, "Lower Bounds To Error Probability For Coding On Discrete Memoryless Channels I", Inform. Control, 10: 65-103.

Berlekamp, E.R., 1967, "The Enumeration of Information Symbols in BCH Codes", Bell System Tech. J., 46:1861-1880.

Berlekamp, E.R., l966, "Two Identical Binary Erasure Channels With Feedback Are Exponentially Better Than One Channel At Low Rates", JPL SPS 37-37, Vo. IV, Section 31.

Berlekamp, E.R., 1965, "On Decoding Bose-Chaudhuri-Hocquenghem Codes", IEEE Trans. Inform. Theory, IT 11: 577-579.

Berlekamp, E.R., 1964, "Note On Recurrent Codes", IEEE Trans. Inform. Theory, IT 10: 257-258.

Berlekamp, E. R., 1964, "Block Coding with Noiseless Feedback", thesis

Berlekamp, E.R., 1963, "A Class of Convolutional Codes", Inform. Control, 6:1-13.

 

Games: Journal Articles, Conference Proceedings, and Technical Reports

Berlekamp, E., 2018, Temperatures of Games and Coupons, to appear in "Games of No Chance 5"

Berlekamp, E. and Low, R.M., "Entrepreneurial Chess", in Int. Journal of Game Theory. 47 (2018), 379-415.

Berlekamp, E., 2009 "Yellow-Brown Hackenbush", in Games of No Chance 3, Michael Albert and Richard Nowakowski, ed; Cambridge University Press, Mathematical Sciences Research Institute Publications 56, 413-418

Berlekamp, E., 2006, "Baduk + Coupons", in ICOB 2006 - The 4th International Conference on Baduk, published by CyberOro, pp. 39-55

Berlekamp, E. 2002 "Four Games for Gardner", in Puzzlers' Tribute: a Feast for the Mind, David Wolfe and Tom Rodgers, editors; published by A K Peters, Ltd., 2002.

Teigo Nakamura and Elwyn Berlekamp, "Analysis of Composite Corridors", Proceedings of the 3rd International Conference on Computers and Games (CG2002), 2002. (lecture slides)

Berlekamp, E., and K. Scott, 2002, "Forcing Your Opponent To Stay In Control Of A Loony Dots-And-Boxes Endgame", in More Games of No Chance, Richard Nowakowski, ed; Cambridge University Press, Mathematical Sciences Research Institute Publications 42, 317-330.

Berlekamp, E., 2002, "Idempotents Among Partisan Games", in More Games of No Chance, Richard Nowakowski, ed.; Cambridge University Press, Mathematical Sciences Research Institute Publications 42, 1-23.

Berlekamp, E., 2002, "The 4G4G4G4G4 Problems and Solutions", in More Games of No Chance, Richard Nowakowski, ed; Cambridge University Press, Mathematical Sciences Research Institute Publications 42, 231-241.

Berlekamp, E., 2000 "Sums of N X 2 Amazons", Institute of Mathematics Statistics "Lecture Notes -- Monograph Series", 35:1-34.

Berlekamp, E., and Yonghoan Kim, 1996, "Where is the Thousand Dollar Ko?" in Games of No Chance, Richard Nowakowski, ed; Cambridge University Press, Mathematical Sciences Research Institute Publications 29:203-226.

Berlekamp, E., 1996, "The Economist's View of Combinatorial Games" in Games of No Chance, Richard Nowakowski, ed; Cambridge University Press, Mathematical Sciences Research Institute Publications 29:365-405.

Berlekamp, E.R., Martin Müller, and Bill Spight, 1996 "Generalized Thermography: Algorithms, Implementation, and Application to Go Endgames" TR-96-030, International Computer Science Institute, Berkeley, CA, ISSN 1075-4946. To download, go to item [18] in Müller's online bibliography.

Berlekamp, E.R. and Y. Kim, 1994 "Where is the Thousand Dollar Ko?", GO World, Volume 71, pp. 65-80, Ishi Press

Berlekamp, E.R., 1994, "Introduction to Blockbusting and Domineering" in "The Lighter Side of Mathematics", R. K. Guy and R. E. Woodrow, editors, Mathematics Association of America

Berlekamp, E.R., 1991, "Introductory Overview of Mathematical Go Endgames", in Combinatorial Games,1991 Richard Guy, ed. vol 43 in AMS Short Course Series, American Mathematical Society

Berlekamp, E.R., 1990, "Two-Person, perfect-information Games", 275-288 in The Legacy of John von Neumann, 1990 J. Glimm, J Impagliazzo, and I. Singer, eds Proceedings of Symposia in Pure Mathematics 50:275-288.

Berlekamp, E.R., 1988, "Two-Person, Perfect-Information Games", Proceedings of the John von Neumann Symposium, Hofstra University, June 2, 1988. American Mathematical Society.

Berlekamp, E.R., 1986, "Blockbusting and Domineering", Journal of Combinatorial Theory, Series A, Vol.49, Number 1, pp.67-116, September 1988.

Berlekamp, E.R., 1974, "The Hackenbush Number System For The Compression Of Numerical Data", Inform. Control, 24:134-140.

Berlekamp, E.R., 1972, "Some Recent Results On The Combinatorial Game Called 'Welter's Nim'", pp.203-204 in Proceedings of the Sixth Annual Conference on Information Sciences and Systems, Princeton, New Jersey.

Berlekamp, E.R., 1969, "The Probabilities Of Certain Bridge Hands", Tech Memo, Bell Telephone Laboratories

Berlekamp, E.R., 1968, "Combinatorial Games, I. Hex, Bridgit, and Shannon's Switching Game", Tech. Memo, Bell Telephone Laboratories

Berlekamp, E.R., 1963, "Program For Double Dummy Bridge -- A New Strategy For Mechanical Game Playing:, JACM, 10:357-364.

Berlekamp, E.R., 1961-1962, weekly bridge columns in MIT's student newspaper, "The Tech".

 

Other: Journal Articles, Conference Proceedings, and Technical Reports

Berlekamp, E., 2014, "The Mathematical Legacy of Martin Gardner", Siam News, September 2014, Volume 47, Number 7, pp 4, 7.

Berlekamp, E., 2009, "In Memoriam: the Galetron", in Games and Economic Behavior, Volume 66, Issue 2 (published by Elsevier).

Berlekamp, E., 2003, "Introduction to Solomon W. Golomb" pgs xi-xiii in "Mathematical Properties of Sequences and Other Combinatorial Structures", Jong-Seon No, Hong-Yeop Song, Tor Helleseth, and P. Vijay Kumar, editors. Kluwer Academic Publications

Berlekamp, E.R., 2003, "Introduction to Solomon W. Golomb - 70", in "Mathematical Properties of Sequences and Other Combinatorial Structures", edited by No, Song, Helleseth and Kumar, Kluwer Academic Publishers, 2003.

Golomb, S., Berlekamp, E.R., Cover, T.M., Gallager, R.G., Massey, J.L., Viterbi, A.J. 2002, " Claude Elwood Shannon (1916-2001)", Notices of the American Mathematical Society, January 2002, 8-16.

Berlekamp, E.R., 2000, "Unimodular Arrays", Computers and Mathematics, 39:77-88 (published by Elsevier).

Berlekamp, E.R., 1993, "1993 Shannon Lecture", Information Theory Society Newsletter, 44: 1, 3-6.

N.J.A. Sloane 1989, "The Solution To Berlekamp's Switching Game", Discrete Mathematics, 74: 263-290.

Berlekamp, E.R., 1986, "If Tennis Players Are Equally Good, Server Has No Advantage", Cyclotomics' Tech memo, September 22, 1986.

Berlekamp, E.R., 1984, "Unsolved Problem", Recent Progress on Combinatorics, Academic Press, 1984.

Berlekamp, E.R., 1976, "Making Change", Mathematics Magazine, 49:195-198.

Berlekamp, E.R., 1976, "Cooperative Bridge Bidding (Corresp.)", IEEE Trans. Inform. Theory, IT 22:753-756.

Berlekamp, E.R., 1976, "An Analog To The Discriminant Over Fields of Characteristic Two", Journal of Algebra, 38:315-317.

Berlekamp, E.R., 1976, "Speedup For The Cray I", Institute For Defense Analysis, Working Paper No. 465

Berlekamp, E.R., 1976, "Merging And Sorting On Cray I", Institute For Defense Analysis, Working Paper No. 464

Berlekamp, E.R., 1976, "Speedup For The CDC 6600", Institute For Defense Analysis, Working Paper No. 463

Berlekamp, E.R., 1975, "The Design of Slowly Shrinking Labelled Squares", Math. of Computation, 29:25-27.

Berlekamp, E.R., H.M. Frederickson, and R.C. Proto, 1974, "Minimum Conditions For Uniquely Determining The Generator of A Linear Sequence", Utilitas Mathematica, 5:305-315.

Berlekamp, E.R., 1974, "The Hackenbush Number System For The Compression of Numerical Data", Inform. Control, 24:134-140.

Berlekamp, E.R., 1973, "Engineering And Public Service", Bridge, Eta Kappa Nu, 69:1-3.

Berlekamp, E.R., J.H. Van Lint, and J.J. Seidel, 1973, "A Strongly Regular Graph Derived From The Perfect Ternary Golay Code", Chapter 3 in J.N. Srivastava (ed.), A Survey of Combinatorial Theory, North-Holland/American Elsevier, Amsterdam.

Berlekamp, E.R., 1973, "An Asymptomatic Expansion For The Quantization Error Of Closely Spaced Uniform Quantizers with Gaussian Input", UCB College of Engineering and Electronic Research Lab, Memo ERL-M381.

Berlekamp, E.R., and F.K. Hwang, 1972, Constructions For Balanced Howell Rotations For Bridge Tournaments", J. Combinatorial Theory, 12:159-165.

Berlekamp, E.R., 1972, "Factoring Polynomials", pp. 1-7 in F. Hoffman, R.B. Levow, and R.S.D. Thomas (eds.), Proc. of the 3rd Southeastern Conference on Combinatorics, GRAPH THEORY AND COMPUTING, Atlantic Univ., Boca Raton, Florida.

Berlekamp, E.R., and R.L. Graham, 1970, "Irregularities In The Distribution of Finite Sequences", J. Number Theory, 2:152161.

Berlekamp, E.R., 1970, "Some Mathematical Properties of a Scheme For Reducing The Bandwidth of Motion Pictures By Hadamard Smearing", Bell System Tech. J., 59:979-986.

Berlekamp, E.R., 1970, "On Sets of Ternary Vectors Whose Only Linear Dependencies Involve An Odd Number of Vectors", Can. Math. Bull., 13:363-366.

Berlekamp, E.R., 1970, "Factoring Polynomials Over Large Finite Fields", Math. of Computation, 24:713-735.

Berlekamp, E.R., and D.D. Sullivan, 1970, "Some Results On Normalized Truncation Groups", pp. 1-1-1 in Proc. of the Univ. of Missouri at Rolla M.J. Kelly Communications Conference.

Berlekamp, E.R., 1970, "Burst Properties Of Certain Linear Binary Codes", Bell Telephone Laboratories, Inc. Murray Hill, NJ, MM70-1216-2, Case 20878-4, January 15, 1970.

Berlekamp, E.R., 1969, "On Subsets With Intersections of Even Cardinality", Can. Math. Bull., 12:471-474.

Berlekamp, E.R., 1968, "A Construction For Partitions Which Avoid Long Arithmetic Progressions", Can. Math. Bull., 11:409414.

Berlekamp, E.R., 1968, "Grundy Functions For Certain Classes of Vines". Tech. memo, Bell Telephone Labs.

Berlekamp, E.R., H. Rumsey Jr., and G. Solomon, 1967, "On The Solution of Algebraic Equations Over Finite Fields", Inform. Control,10:553-564.

Berlekamp, E.R., 1967, "Factoring Polynomials Over Finite Fields", Bell System Tech. J., 46:1853-1849.

Culsam, Hwan, and Eman, Hutch, 1967, "Viet Nam - A Revolutionary New Board Game", Copyright 1967 by E. R. Berlekamp.

Berlekamp, E.R., 1966, "Distribution of Cyclic Matrices In A Finite Field:, Duke Math. J., 33:45-48.

Berlekamp, E.R., and L. Kleinrock, 1966, "Analysis of Channels With Unidirectional Drift", JPL Space Programs Summary No. 3739, Vol. IV.

Berlekamp, E.R., E.N. Gilbert, and F.W. Sinden, 1965, "A Polygon Problem", Am. Math. Monthly, 72:233-241.

Berlekamp, E.R., 1963, "Probabilistic Mazes", Bell Telephone Laboratories, Case No. 20878-4, June 20, 1963.

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