TY - JOUR
T1 - Minimal PD-sets for codes associated with the graphs Qm2, m even
AU - Key, J. D.
AU - Rodrigues, B. G.
N1 - Funding Information:
This work is based on the research supported by the National Research Foundation of South Africa (Grant Number 120846).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - For m≥4m≥4 even, the duals of p-ary codes, for any prime p, from adjacency matrices for the m-ary 2-cube Qm2Q2m are shown to have subcodes with parameters [m2,2m−2,m][m2,2m−2,m] for which minimal PD-sets of size m2m2 are constructed, hence attaining the full error-correction capabilities of the code, and, as such, the most efficient sets for full permutation decoding.
AB - For m≥4m≥4 even, the duals of p-ary codes, for any prime p, from adjacency matrices for the m-ary 2-cube Qm2Q2m are shown to have subcodes with parameters [m2,2m−2,m][m2,2m−2,m] for which minimal PD-sets of size m2m2 are constructed, hence attaining the full error-correction capabilities of the code, and, as such, the most efficient sets for full permutation decoding.
KW - LCD codes
KW - Lee graphs
KW - Permutation decoding
UR - http://www.scopus.com/inward/record.url?scp=85099213411&partnerID=8YFLogxK
U2 - 10.1007/s00200-020-00481-5
DO - 10.1007/s00200-020-00481-5
M3 - Article
AN - SCOPUS:85099213411
SN - 0938-1279
VL - 34
SP - 57
EP - 66
JO - Applicable Algebra in Engineering, Communications and Computing
JF - Applicable Algebra in Engineering, Communications and Computing
IS - 1
ER -