Generalized binary arrays from quasi-orthogonal cocycles

Generalized perfect binary arrays (GPBAs) were used by Jedwab to construct perfect binary arrays. A non-trivial GPBA can exist only if its energy is \(2\) or a multiple of \(4\). This paper introduces generalized optimal binary arrays (GOBAs) with even energy not divisible by \(4\), as analogs of GP...

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Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: Armario, J A, Flannery, D L
Format: Article
Language:English
Subjects:
Arrays
Binary system
Online Access:Get full text
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Summary:Generalized perfect binary arrays (GPBAs) were used by Jedwab to construct perfect binary arrays. A non-trivial GPBA can exist only if its energy is \(2\) or a multiple of \(4\). This paper introduces generalized optimal binary arrays (GOBAs) with even energy not divisible by \(4\), as analogs of GPBAs. We give a procedure to construct GOBAs based on a characterization of the arrays in terms of \(2\)-cocycles. As a further application, we determine negaperiodic Golay pairs arising from generalized optimal binary sequences of small length.
ISSN:2331-8422
DOI:10.48550/arxiv.1902.08812