Symmetric Weighing Matrices Constructed using Group Matrices

被引：0

作者：

Miin Huey Ang

Siu Lun Ma

机构：

[1] Universiti Sains Malaysia,Pusat Pengajian Sains Matematik

[2] National University of Singapore,Department of Mathematics

来源：

Designs, Codes and Cryptography | 2005年 / 37卷

关键词：

weighing matrices; group matrices; Hadamard matrices; 05B20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A weighing matrix of order n and weight m2 is a square matrix M of order n with entries from {-1,0,+1} such that MMT=m2I where I is the identity matrix of order n. If M is a group matrix constructed using a group of order n, M is called a group weighing matrix. Recently, group weighing matrices were studied intensively, especially when the groups are cyclic and abelian. In this paper, we study the abelian group weighing matrices that are symmetric, i.e.MT=M. Some new examples are found. Also we obtain a few exponent bounds on abelian groups that admit symmetric group weighing matrices. In particular, we prove that there is no symmetric abelian group weighing matrices of order 2pr and weight p2 where p is a prime and p≥ 5.

引用

页码：195 / 210

页数：15

共 18 条

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