Twisted centralizer codes

Adel Alahmadi; S. P. Glasby; Cheryl E. Praeger; Patrick Solé; Bahattin Yildiz

doi:10.1016/j.laa.2017.03.011

Twisted centralizer codes

Adel Alahmadi, S. P. Glasby, Cheryl E. Praeger, Patrick Solé, Bahattin Yildiz

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

6 Scopus citations

Abstract

Given an n×n matrix A over a field F and a scalar a∈F, we consider the linear codes C(A,a):={B∈F^n×n|AB=aBA} of length n². We call C(A,a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a=1) is at most n, however for a≠0,1 the minimal distance can be much larger, as large as n².

Original language	English (US)
Pages (from-to)	235-249
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	524
DOIs	https://doi.org/10.1016/j.laa.2017.03.011
State	Published - Jul 1 2017
Externally published	Yes

Keywords

Group centralizers
Linear codes
Matrix codes
Minimal distance

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2017.03.011

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title = "Twisted centralizer codes",

abstract = "Given an n×n matrix A over a field F and a scalar a∈F, we consider the linear codes C(A,a):={B∈Fn×n|AB=aBA} of length n2. We call C(A,a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a=1) is at most n, however for a≠0,1 the minimal distance can be much larger, as large as n2.",

keywords = "Group centralizers, Linear codes, Matrix codes, Minimal distance",

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AU - Alahmadi, Adel

AU - Glasby, S. P.

AU - Praeger, Cheryl E.

AU - Solé, Patrick

AU - Yildiz, Bahattin

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Given an n×n matrix A over a field F and a scalar a∈F, we consider the linear codes C(A,a):={B∈Fn×n|AB=aBA} of length n2. We call C(A,a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a=1) is at most n, however for a≠0,1 the minimal distance can be much larger, as large as n2.

AB - Given an n×n matrix A over a field F and a scalar a∈F, we consider the linear codes C(A,a):={B∈Fn×n|AB=aBA} of length n2. We call C(A,a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a=1) is at most n, however for a≠0,1 the minimal distance can be much larger, as large as n2.

KW - Group centralizers

KW - Linear codes

KW - Matrix codes

KW - Minimal distance

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Twisted centralizer codes

Abstract

Keywords

ASJC Scopus subject areas

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