Twisted centralizer codes

Adel Alahmadi, S. P. Glasby, Cheryl E. Praeger, Patrick Solé, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Given an n×n matrix A over a field F and a scalar a∈F, we consider the linear codes C(A,a):={B∈Fn×n|AB=aBA} of length n2. We call C(A,a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a=1) is at most n, however for a≠0,1 the minimal distance can be much larger, as large as n2.

Original languageEnglish (US)
Pages (from-to)235-249
Number of pages15
JournalLinear Algebra and Its Applications
StatePublished - Jul 1 2017
Externally publishedYes


  • Group centralizers
  • Linear codes
  • Matrix codes
  • Minimal distance

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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