A note on Assmus–Mattson type theorems

Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

研究成果: ジャーナルへの寄稿学術論文査読

12 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)843-858
ページ数16
ジャーナルDesigns, Codes, and Cryptography
89
5
DOI
出版ステータス出版済み - 2021 5月

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