Twisted centralizer codes

Adel Alahmadi; Stephen Glasby; Cheryl Praeger; Patrick Sole; Bahattin Yildiz

doi:10.1016/j.laa.2017.03.011

Twisted centralizer codes

Adel Alahmadi, Stephen Glasby, Cheryl Praeger, Patrick Sole, Bahattin Yildiz

Information, Technology (IT) & Systems

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

5 Citations (Scopus)

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.

Original language	English
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
Publication status	Published - 1 Jul 2017

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10.1016/j.laa.2017.03.011

https://arxiv.org/pdf/1608.04079.pdf

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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 = "automorphism groups, Group centralizers, Matrix codes, Linear codes, Minimal distance",

author = "Adel Alahmadi and Stephen Glasby and Cheryl Praeger and Patrick Sole and Bahattin Yildiz",

note = "Publisher Copyright: {\textcopyright} 2017",

year = "2017",

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doi = "10.1016/j.laa.2017.03.011",

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T1 - Twisted centralizer codes

AU - Alahmadi, Adel

AU - Glasby, Stephen

AU - Praeger, Cheryl

AU - Sole, 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 - automorphism groups

KW - Group centralizers

KW - Matrix codes

KW - Linear codes

KW - Minimal distance

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U2 - 10.1016/j.laa.2017.03.011

DO - 10.1016/j.laa.2017.03.011

M3 - Article

VL - 524

SP - 235

EP - 249

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

Twisted centralizer codes

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