Singly even self-dual codes of length $24k+10$ and minimum weight $4k+2$
Combinatorics
2020-11-20 v1 Information Theory
math.IT
Abstract
Currently, the existence of an extremal singly even self-dual code of length is unknown for all nonnegative integers . In this note, we study singly even self-dual codes. We give some restrictions on the possible weight enumerators of singly even self-dual codes with shadows of minimum weight at least for . We discuss a method for constructing singly even self-dual codes with minimal shadow. As an example, a singly even self-dual code with minimal shadow is constructed for the first time. In addition, as neighbors of the code, we construct singly even self-dual codes with weight enumerator for which no singly even self-dual code was previously known to exist.
Cite
@article{arxiv.1804.02129,
title = {Singly even self-dual codes of length $24k+10$ and minimum weight $4k+2$},
author = {Masaaki Harada},
journal= {arXiv preprint arXiv:1804.02129},
year = {2020}
}
Comments
16 pages