TY - JOUR

T1 - Twisted centralizer codes

AU - Alahmadi, Adel

AU - Glasby, Stephen

AU - Praeger, Cheryl

AU - Sole, Patrick

AU - Yildiz, Bahattin

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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.

AB - 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.

KW - automorphism groups

U2 - 10.1016/j.laa.2017.03.011

DO - 10.1016/j.laa.2017.03.011

M3 - Article

VL - 524

SP - 235

EP - 249

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -