Centraliser codes

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)68-77
Number of pages10
JournalLinear Algebra and Its Applications
StatePublished - Dec 15 2014
Externally publishedYes


  • 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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