TY - JOUR

T1 - Centraliser codes

AU - Alahmadi, A.N.

AU - Alamoudi, S.

AU - Karadeniz, S.

AU - Yıldız, B.

AU - Praeger, Cheryl

AU - Solé, P.

PY - 2014

Y1 - 2014

N2 - © 2014 Elsevier Inc. 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 - © 2014 Elsevier Inc. 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.

U2 - 10.1016/j.laa.2014.08.024

DO - 10.1016/j.laa.2014.08.024

M3 - Article

VL - 463

SP - 68

EP - 77

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -