Structure of group invariant weighing matrices of small weight
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 boun...
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sg-ntu-dr.10356-877212023-02-28T19:34:48Z Structure of group invariant weighing matrices of small weight Leung, Ka Hin Schmidt, Bernhard School of Physical and Mathematical Sciences Smith Normal Form Unique Differences 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. Accepted version 2018-03-01T09:21:35Z 2019-12-06T16:47:56Z 2018-03-01T09:21:35Z 2019-12-06T16:47:56Z 2017 Journal Article Leung, K. H., & Schmidt, B. (2018). Structure of group invariant weighing matrices of small weight. Journal of Combinatorial Theory, Series A, 154, 114-128. 0097-3165 https://hdl.handle.net/10356/87721 http://hdl.handle.net/10220/44477 10.1016/j.jcta.2017.08.016 en Journal of Combinatorial Theory, Series A © 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]. 19 p. application/pdf |
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Smith Normal Form Unique Differences |
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Smith Normal Form Unique Differences Leung, Ka Hin Schmidt, Bernhard Structure of group invariant weighing matrices of small weight |
| description |
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. |
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School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Leung, Ka Hin Schmidt, Bernhard |
| format |
Article |
| author |
Leung, Ka Hin Schmidt, Bernhard |
| author_sort |
Leung, Ka Hin |
| title |
Structure of group invariant weighing matrices of small weight |
| title_short |
Structure of group invariant weighing matrices of small weight |
| title_full |
Structure of group invariant weighing matrices of small weight |
| title_fullStr |
Structure of group invariant weighing matrices of small weight |
| title_full_unstemmed |
Structure of group invariant weighing matrices of small weight |
| title_sort |
structure of group invariant weighing matrices of small weight |
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2018 |
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https://hdl.handle.net/10356/87721 http://hdl.handle.net/10220/44477 |
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