Abstract
Centraliser codes are codes of length n(2) 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. (C) 2014 Elsevier Inc. All rights reserved.