Structure of group invariant weighing matrices of small weight

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:154

Article

Leung, Ka Hin¹  Schmidt, Bernhard² 

[1] Natl Univ Singapore, Dept Math, Singapore 119260, Singapore

[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

关键词: Unique differences;    Smith normal form;    Weighing matrices;   

DOI  :  10.1016/j.jcta.2017.08.016

来源: Elsevier

【 摘 要 】

We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with vertical bar H vertical bar <= 2(n-1). Furthermore, if n is an odd prime power and a proper circulant weighing matrix of weight n and order v exists, then v <= 2(n-1). We also obtain a lower bound on the weight of group invariant matrices depending on the invariant factors of the underlying group. These results are obtained by investigating the structure of subsets of finite abelian groups that do not have unique differences. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free