Generalized binary arrays from quasi-orthogonal cocycles

J. A. Armario; D. L. Flannery

doi:10.1007/s10623-019-00626-9

Generalized binary arrays from 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

4 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2405-2417
Number of pages	13
Journal	Designs, Codes, and Cryptography
Volume	87
Issue number	10
DOIs	https://doi.org/10.1007/s10623-019-00626-9
Publication status	Published - 1 Oct 2019

Keywords

(Quasi)-orthogonal
Autocorrelation
Cocycle
Difference set
Generalized optimal binary arrays
Negaperiodic Golay pair

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10.1007/s10623-019-00626-9

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abstract = "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.",

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AU - Flannery, D. L.

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N2 - 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.

AB - 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.

KW - (Quasi)-orthogonal

KW - Autocorrelation

KW - Cocycle

KW - Difference set

KW - Generalized optimal binary arrays

KW - Negaperiodic Golay pair

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DO - 10.1007/s10623-019-00626-9

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JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 10

ER -

Generalized binary arrays from quasi-orthogonal cocycles

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Keywords

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