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
SN - 0024-3795
VL - 463
SP - 68
EP - 77
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -