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arXiv · 1212.3467

Improved Semidefinite Programming Bound on Sizes of Codes

Hyun Kwang Kim·Phan Thanh Toan
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Abstract

Let $A(n,d)$ (respectively $A(n,d,w)$) be the maximum possible number of codewords in a binary code (respectively binary constant-weight $w$ code) of length $n$ and minimum Hamming distance at least $d$. By adding new linear constraints to Schrijver's semidefinite programming bound, which is obtained from block-diagonalising the Terwilliger algebra of the Hamming cube, we obtain two new upper bounds on $A(n,d)$, namely $A(18,8) \leq 71$ and $A(19,8) \leq 131$. Twenty three new upper bounds on $A(n,d,w)$ for $n \leq 28$ are also obtained by a similar way.

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Hyun Kwang Kim, Phan Thanh Toan. 2012-12-14. Improved Semidefinite Programming Bound on Sizes of Codes. https://arxiv.org/abs/1212.3467

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