A sensitive algorithm for detecting the inequivalence of Hadamard matrices

被引:0
|
作者
Fang, KT [1 ]
Ge, GN
机构
[1] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
[2] Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China
关键词
algorithm; equivalence; Hadamard matrix; Hamming distance; uniformity;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A Hadamard matrix of side n is an n x n matrix with every entry either 1 or -1, which satisfies HHT = nI. Two Hadamard matrices are called equivalent if one can be obtained from the other by some sequence of row and column permutations and negations. To identify the equivalence of two Hadamard matrices by a complete search is known to be an NP hard problem when n increases. In this paper, a new algorithm for detecting inequivalence of two Hadamard matrices is proposed, which is more sensitive than those known in the literature and which has a close relation with several measures of uniformity. As an application, we apply the new algorithm to verify the inequivalence of the known 60 inequivalent Hadamard matrices of order 24; furthermore, we show that there are at least 382 pairwise inequivalent Hadamard matrices of order 36. The latter is a new discovery.
引用
收藏
页码:843 / 851
页数:9
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