On triply even binary codes
Combinatorics
2012-10-02 v3
Abstract
A triply even code is a binary linear code in which the weight of every codeword is divisible by 8. We show how two doubly even codes of lengths m_1 and m_2 can be combined to make a triply even code of length m_1+m_2, and then prove that every maximal triply even code of length 48 can be obtained by combining two doubly even codes of length 24 in a certain way. Using this result, we show that there are exactly 10 maximal triply even codes of length 48 up to equivalence.
Keywords
Cite
@article{arxiv.1012.4134,
title = {On triply even binary codes},
author = {Koichi Betsumiya and Akihiro Munemasa},
journal= {arXiv preprint arXiv:1012.4134},
year = {2012}
}
Comments
21 pages + appendix of 10 pages. Minor revision