New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction
Information Theory
2023-03-24 v2 Combinatorics
math.IT
Abstract
In this paper, we present a new bordered construction for self-dual codes which employs -circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring of characteristic 2. Moreover, using our bordered construction together with the well-known building-up and neighbour methods, we construct many binary self-dual codes of lengths 56, 62, 78, 92 and 94 with parameters in their weight enumerators that were not known in the literature before.
Cite
@article{arxiv.2108.09184,
title = {New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction},
author = {Joe Gildea and Adrian Korban and Adam Michael Roberts and Alexander Tylyshchak},
journal= {arXiv preprint arXiv:2108.09184},
year = {2023}
}
Comments
corrected typos; other minor corrections. arXiv admin note: substantial text overlap with arXiv:2102.10354, arXiv:2106.12355, arXiv:2102.12326