2016/08/14 by Adel Alahmadi, Alahmadi, Adel, S. P. Glasby +7
Computer Science · Mathematics · #13M05 #94B05 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.AC #math.CO #math.IT #msc:13M05 #msc:94B05
paper · pdf · doi:10.48550/arxiv.1608.04079
14 pages. Proof of Proposition 2.6 corrected (see last 3 lines). Email address of last author changed
arxiv created 2017/03/12 · arxiv updated 2017/03/14
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.