A group induced four-circulant construction for self-dual codes and new extremal binary self-dual codes
Combinatorics
2019-12-30 v1 Information Theory
math.IT
Abstract
We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F_2 + uF_2 and F_4 + uF_4; using groups of order 3, 7, 9, 13, and 15. Through these constructions and their extensions, we find binary self-dual codes of lengths 32, 40, 56, 64, 68 and 80, all of which are extremal or optimal. In particular, we find five new self-dual codes of parameters [56, 28, 10], twenty-three extremal binary self-dual codes of length 68 with new weight enumerators and fifteen new self-dual codes of parameters [80, 40, 14].
Keywords
Cite
@article{arxiv.1912.11758,
title = {A group induced four-circulant construction for self-dual codes and new extremal binary self-dual codes},
author = {Joe Gildea and Abidin Kaya and Alexander Tylyshchak and Bahattin Yildiz},
journal= {arXiv preprint arXiv:1912.11758},
year = {2019}
}