A circulant approach to skew-constacyclic codes

Neville Fogarty; Heide Gluesing-Luerssen

doi:10.1016/j.ffa.2015.03.008

A circulant approach to skew-constacyclic codes

Neville Fogarty, Heide Gluesing-Luerssen

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;θ] modulo the left ideal generated by a polynomial of the form ^xn-a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where xⁿ-a is central.

Original language	English
Pages (from-to)	92-114
Number of pages	23
Journal	Finite Fields and Their Applications
Volume	35
DOIs	https://doi.org/10.1016/j.ffa.2015.03.008
State	Published - Sep 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Funding

Funders	Funder number
Not added	1210061

Keywords

Circulants
Linear block codes
Skew-cyclic codes
Skew-polynomial rings

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1016/j.ffa.2015.03.008

Cite this

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title = "A circulant approach to skew-constacyclic codes",

abstract = "We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;θ] modulo the left ideal generated by a polynomial of the form xn-a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where xn-a is central.",

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doi = "10.1016/j.ffa.2015.03.008",

language = "English",

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T1 - A circulant approach to skew-constacyclic codes

AU - Fogarty, Neville

AU - Gluesing-Luerssen, Heide

PY - 2015/9/1

Y1 - 2015/9/1

N2 - We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;θ] modulo the left ideal generated by a polynomial of the form xn-a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where xn-a is central.

AB - We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;θ] modulo the left ideal generated by a polynomial of the form xn-a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where xn-a is central.

KW - Circulants

KW - Linear block codes

KW - Skew-cyclic codes

KW - Skew-polynomial rings

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DO - 10.1016/j.ffa.2015.03.008

M3 - Article

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SN - 1071-5797

VL - 35

SP - 92

EP - 114

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

ER -

A circulant approach to skew-constacyclic codes

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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