TY - JOUR
T1 - Twisted centralizer codes
AU - Alahmadi, Adel
AU - Glasby, S. P.
AU - Praeger, Cheryl E.
AU - Solé, 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 - Group centralizers
KW - Linear codes
KW - Matrix codes
KW - Minimal distance
UR - http://www.scopus.com/inward/record.url?scp=85015453641&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2017.03.011
DO - 10.1016/j.laa.2017.03.011
M3 - Article
AN - SCOPUS:85015453641
VL - 524
SP - 235
EP - 249
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -