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 |