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arXiv · 2002.11353

A note on Assmus--Mattson type theorems

Tsuyoshi Miezaki·Akihiro Munemasa·Hiroyuki Nakasora
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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.

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Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora. 2020-12-20. A note on Assmus--Mattson type theorems. https://arxiv.org/abs/2002.11353

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