New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming

作     者：Gijswijt, Dion Schrijver, Alexander Tanaka, Hajime 

作者机构：Univ Amsterdam Dept Math NL-1018 TV Amsterdam Netherlands CWI NL-1098 SJ Amsterdam Netherlands Tohoku Univ Grad Sch Informat Sci Div Math Sendai Miyagi 980 Japan 

出 版 物：《JOURNAL OF COMBINATORIAL THEORY SERIES A》 (组合理论杂志，Ａ辑)

年 卷 期：2006年第113卷第8期

页      面：1719-1731页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：codes nonbinary codes upper bounds Delsarte bound Terwilliger algebra block-diagonalization semidefinite programming 

摘      要：We give a new upper bound on the maximum size A(q) (n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q = 3 letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q = 3, 4, 5 this gives several improved upper bounds for concrete values of n and d. This work builds upon previous results of Schrijver [A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (2005) 2859-2866] on the Terwilliger algebra of the binary Hamming scheme. (c) 2006 Elsevier Inc. All rights reserved.