A note on Assmus--Mattson type theorems
Combinatorics
2020-12-22 v2 Group Theory
Number Theory
Abstract
In the present paper, we give Assmus--Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m with minimum norm 2m provides a spherical 3-design. We remark that some of such codes and lattices give t-designs for higher t. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24m with minimum weight 4m. Ternary and quaternary analogues are also given.
Cite
@article{arxiv.2002.11353,
title = {A note on Assmus--Mattson type theorems},
author = {Tsuyoshi Miezaki and Akihiro Munemasa and Hiroyuki Nakasora},
journal= {arXiv preprint arXiv:2002.11353},
year = {2020}
}
Comments
17 pages