Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
Information Theory
2023-01-18 v1 Combinatorics
math.IT
Abstract
In this work, we define a modification of a bordered construction for self-dual codes which utilises -circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. Using the modified construction together with the neighbour construction, we construct many binary self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have previously not been known to exist.
Keywords
Cite
@article{arxiv.2109.00908,
title = {Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours},
author = {Joe Gildea and Adrian Korban and Adam Michael Roberts and Alexander Tylyshchak},
journal= {arXiv preprint arXiv:2109.00908},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2108.09184, arXiv:2106.12355, arXiv:2102.10354