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

Access to Document

10.1016/j.laa.2017.03.011

Cite this

@article{771116d4909545ce8440f10f485b4236,

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",

author = "Adel Alahmadi and Glasby, \{S. P.\} and Praeger, \{Cheryl E.\} and Patrick Sol{\'e} and Bahattin Yildiz",

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

year = "2017",

month = jul,

day = "1",

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

language = "English (US)",

volume = "524",

pages = "235--249",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Twisted centralizer codes

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

UR - https://www.scopus.com/pages/publications/85015453641

UR - https://www.scopus.com/inward/citedby.url?scp=85015453641&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2017.03.011

DO - 10.1016/j.laa.2017.03.011

M3 - Article

AN - SCOPUS:85015453641

SN - 0024-3795

VL - 524

SP - 235

EP - 249

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Twisted centralizer codes

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this