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

3 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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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

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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.

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10.1016/j.laa.2017.03.011