New binary self-dual codes via a generalization of the four circulant construction
Combinatorics
2019-12-30 v1 Information Theory
math.IT
Abstract
In this work, we generalize the four circulant construction for self-dual codes. By applying the constructions over the alphabets F_2, F_2 + uF_2, F_4+uF_4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed.
Keywords
Cite
@article{arxiv.1912.11754,
title = {New binary self-dual codes via a generalization of the four circulant construction},
author = {Joe Gildea and Abidin Kaya and Bahattin Yildiz},
journal= {arXiv preprint arXiv:1912.11754},
year = {2019}
}