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 -