On quasi-orthogonal cocycles

J. A. Armario; D. L. Flannery

doi:10.1002/jcd.21597

On quasi-orthogonal cocycles

J. A. Armario, D. L. Flannery

Mathematics

University of Sevilla

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

6 Citations (Scopus)

Abstract

We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square {±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.

Original language	English
Pages (from-to)	401-411
Number of pages	11
Journal	Journal of Combinatorial Designs
Volume	26
Issue number	8
DOIs	https://doi.org/10.1002/jcd.21597
Publication status	Published - Aug 2018

Keywords

(quasi-)Hadamard group
(quasi-)orthogonal
block design
cocycle
difference set

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10.1002/jcd.21597

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AB - We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square {±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.

KW - (quasi-)Hadamard group

KW - (quasi-)orthogonal

KW - block design

KW - cocycle

KW - difference set

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DO - 10.1002/jcd.21597

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JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 8

ER -

On quasi-orthogonal cocycles

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Keywords

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