TY - JOUR

T1 - Bounds for Binary Codes of Length Less Than 25

AU - Best, M. R.

AU - Brouwer, A. E.

AU - Macwilliams, F. Jessie

AU - Odlyzko, Andrew M.

AU - Sloane, Neil J.A.

PY - 1978/1

Y1 - 1978/1

N2 - 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).

AB - 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).

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U2 - 10.1109/TIT.1978.1055827

DO - 10.1109/TIT.1978.1055827

M3 - Article

AN - SCOPUS:0017926560

VL - 24

SP - 81

EP - 93

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

ER -