Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777463 | Journal of Combinatorial Theory, Series A | 2018 | 15 Pages |
Abstract
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 |H|â¤2nâ1. Furthermore, if n is an odd prime power and a proper circulant weighing matrix of weight n and order v exists, then vâ¤2nâ1. 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ka Hin Leung, Bernhard Schmidt,