### Abstract

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 language | English |
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Pages (from-to) | 235-249 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 524 |

DOIs | |

Publication status | Published - 1 Jul 2017 |

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## Cite this

Alahmadi, A., Glasby, S., Praeger, C., Sole, P., & Yildiz, B. (2017). Twisted centralizer codes.

*Linear Algebra and Its Applications*,*524*, 235-249. https://doi.org/10.1016/j.laa.2017.03.011