On quasi-orthogonal cocycles

We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square \(\{\pm 1\}\)-matrices of size congruent to \(2\) modulo \(4\). Quasi-orthogonal cocycles are analogous to the orthogonal cocycles of algebraic design theory. Equivalences wit...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Authors: Armario, J A, Flannery, D L
Format: Article
Language:English
Subjects:
Combinatorial analysis
Online Access:Get full text
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Summary:We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square \(\{\pm 1\}\)-matrices of size congruent to \(2\) modulo \(4\). Quasi-orthogonal cocycles are analogous to the orthogonal cocycles of algebraic design theory. Equivalences with new and known combinatorial objects afforded by this analogy, such as quasi-Hadamard groups, relative quasi-difference sets, and certain partially balanced incomplete block designs, are proved.
ISSN:2331-8422
DOI:10.48550/arxiv.1902.08808