New cubic self-dual codes of length 54, 60 and 66
Number Theory
2017-06-26 v1 Information Theory
math.IT
Abstract
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50 new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more binary cubic self-dual codes with length 54, 60 and 66.
Cite
@article{arxiv.1706.07631,
title = {New cubic self-dual codes of length 54, 60 and 66},
author = {Pınar Çomak and Jon-Lark Kim and Ferruh Özbudak},
journal= {arXiv preprint arXiv:1706.07631},
year = {2017}
}
Comments
8 pages