Twisted centralizer codes

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

Research output: Contribution to journalArticle

2 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 languageEnglish
Pages (from-to)235-249
Number of pages15
JournalLinear Algebra and Its Applications
Volume524
DOIs
Publication statusPublished - 1 Jul 2017

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Centralizer
Linear Codes
Minimum Distance
Automorphism Group
Parity
Scalar

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Alahmadi, A., Glasby, S., Praeger, C., Sole, P., & Yildiz, B. (2017). Twisted centralizer codes. Linear Algebra and Its Applications, 524, 235-249. https://doi.org/10.1016/j.laa.2017.03.011
Alahmadi, Adel ; Glasby, Stephen ; Praeger, Cheryl ; Sole, Patrick ; Yildiz, Bahattin. / Twisted centralizer codes. In: Linear Algebra and Its Applications. 2017 ; Vol. 524. pp. 235-249.
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Alahmadi, A, Glasby, S, Praeger, C, Sole, P & Yildiz, B 2017, 'Twisted centralizer codes', Linear Algebra and Its Applications, vol. 524, pp. 235-249. https://doi.org/10.1016/j.laa.2017.03.011

Twisted centralizer codes. / Alahmadi, Adel; Glasby, Stephen; Praeger, Cheryl; Sole, Patrick; Yildiz, Bahattin.

In: Linear Algebra and Its Applications, Vol. 524, 01.07.2017, p. 235-249.

Research output: Contribution to journalArticle

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T1 - Twisted centralizer codes

AU - Alahmadi, Adel

AU - Glasby, Stephen

AU - Praeger, Cheryl

AU - Sole, Patrick

AU - Yildiz, Bahattin

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Alahmadi A, Glasby S, Praeger C, Sole P, Yildiz B. Twisted centralizer codes. Linear Algebra and Its Applications. 2017 Jul 1;524:235-249. https://doi.org/10.1016/j.laa.2017.03.011