Bounds for Binary Codes of Length Less Than 25

M. R. Best, A. E. Brouwer, F. Jessie Macwilliams, Andrew M. Odlyzko, Neil J.A. Sloane

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Abstract

Improved bounds for A(n,d), the maximum number of codewords in a (linear or nonlinear) binary code of word length n and minimum distance d, and for A(n,d,w), the maximum number of binary vectors of length n, distance d, and constant weight w in the range n ≤ 24 and d ≤ 10 are presented. Some of the new values are A (9,4) = 20 (which was previously believed to follow from the results of Wax), A (13,6) = 32 (which proves that the Nadler code is optimal), A (17,8) = 36 or 37, and A (21,8) = 512. The upper bounds on A (n,d) are found with the help of linear programming, making use of the values of A (n,d,w).

Original languageEnglish (US)
Pages (from-to)81-93
Number of pages13
JournalIEEE Transactions on Information Theory
Volume24
Issue number1
DOIs
StatePublished - Jan 1978

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    Best, M. R., Brouwer, A. E., Macwilliams, F. J., Odlyzko, A. M., & Sloane, N. J. A. (1978). Bounds for Binary Codes of Length Less Than 25. IEEE Transactions on Information Theory, 24(1), 81-93. https://doi.org/10.1109/TIT.1978.1055827