Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/87721
Title: Structure of group invariant weighing matrices of small weight
Authors: Leung, Ka Hin
Schmidt, Bernhard
Keywords: Smith Normal Form
Unique Differences
Issue Date: 2017
Source: Leung, K. H., & Schmidt, B. (2018). Structure of group invariant weighing matrices of small weight. Journal of Combinatorial Theory, Series A, 154, 114-128.
Series/Report no.: Journal of Combinatorial Theory, Series A
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|≤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.
URI: https://hdl.handle.net/10356/87721
http://hdl.handle.net/10220/44477
ISSN: 0097-3165
DOI: http://dx.doi.org/10.1016/j.jcta.2017.08.016
Rights: © 2017 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Combinatorial Theory, Series A, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.jcta.2017.08.016].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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