Centraliser codes

Adel Alahmadi; Shefa Alamoudi; Suat Karadeniz; Bahattin Yildiz; Cheryl Praeger; Patrick Solé

doi:10.1016/j.laa.2014.08.024

Centraliser codes

Adel Alahmadi, Shefa Alamoudi, Suat Karadeniz, Bahattin Yildiz, Cheryl Praeger, Patrick Solé

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

5 Scopus citations

Abstract

Centraliser codes are codes of length ⁿ² defined as centralisers of a given matrix A of order n. Their dimension, parity-check matrices, syndromes, and automorphism groups are investigated. A lower bound on the dimension is n, the order of A. This bound is met when the minimal polynomial is equal to the annihilator, i.e. for so-called cyclic (a.k.a. non-derogatory) matrices. If, furthermore, the matrix is separable and the adjacency matrix of a graph, the automorphism group of that graph is shown to be abelian and to be even trivial if the alphabet field is of even characteristic.

Original language	English (US)
Pages (from-to)	68-77
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	463
DOIs	https://doi.org/10.1016/j.laa.2014.08.024
State	Published - Dec 15 2014
Externally published	Yes

Keywords

Cyclic matrices
Group centralisers
Matrix codes
Separable matrices

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.2014.08.024

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title = "Centraliser codes",

abstract = "Centraliser codes are codes of length n2 defined as centralisers of a given matrix A of order n. Their dimension, parity-check matrices, syndromes, and automorphism groups are investigated. A lower bound on the dimension is n, the order of A. This bound is met when the minimal polynomial is equal to the annihilator, i.e. for so-called cyclic (a.k.a. non-derogatory) matrices. If, furthermore, the matrix is separable and the adjacency matrix of a graph, the automorphism group of that graph is shown to be abelian and to be even trivial if the alphabet field is of even characteristic.",

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doi = "10.1016/j.laa.2014.08.024",

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T1 - Centraliser codes

AU - Alahmadi, Adel

AU - Alamoudi, Shefa

AU - Karadeniz, Suat

AU - Yildiz, Bahattin

AU - Praeger, Cheryl

AU - Solé, Patrick

PY - 2014/12/15

Y1 - 2014/12/15

N2 - Centraliser codes are codes of length n2 defined as centralisers of a given matrix A of order n. Their dimension, parity-check matrices, syndromes, and automorphism groups are investigated. A lower bound on the dimension is n, the order of A. This bound is met when the minimal polynomial is equal to the annihilator, i.e. for so-called cyclic (a.k.a. non-derogatory) matrices. If, furthermore, the matrix is separable and the adjacency matrix of a graph, the automorphism group of that graph is shown to be abelian and to be even trivial if the alphabet field is of even characteristic.

AB - Centraliser codes are codes of length n2 defined as centralisers of a given matrix A of order n. Their dimension, parity-check matrices, syndromes, and automorphism groups are investigated. A lower bound on the dimension is n, the order of A. This bound is met when the minimal polynomial is equal to the annihilator, i.e. for so-called cyclic (a.k.a. non-derogatory) matrices. If, furthermore, the matrix is separable and the adjacency matrix of a graph, the automorphism group of that graph is shown to be abelian and to be even trivial if the alphabet field is of even characteristic.

KW - Cyclic matrices

KW - Group centralisers

KW - Matrix codes

KW - Separable matrices

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DO - 10.1016/j.laa.2014.08.024

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SP - 68

EP - 77

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Centraliser codes

Abstract

Keywords

ASJC Scopus subject areas

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