In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form [In | {\Omega}(v)], where In is the identity matrix and {\Omega}(v) is a composite matrix and search for binary self-dual codes with parameters [36, 18, 6 or 8]. We next lift these codes over the ring R1 = F2 + uF2 to obtain codes whose binary images are self-dual codes with parameters [72,36,12]. Many of these codes turn out to have weight enumerators with parameters that were not known in the literature before. In particular, we find 30 new Type I binary self-dual codes with parameters [72, 36, 12].
@article{arxiv.2102.00474,
title = {New Type I Binary [72, 36, 12] Self-Dual Codes from Composite Matrices and R1 Lifts},
author = {Adrian Korban and Serap Sahinkaya and Deniz Ustun},
journal= {arXiv preprint arXiv:2102.00474},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:2003.05064, arXiv:2002.11614