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Published in: Designs, Codes and Cryptography 5/2021

23-02-2021

A note on Assmus–Mattson type theorems

Authors: Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

Published in: Designs, Codes and Cryptography | Issue 5/2021

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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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Metadata
Title
A note on Assmus–Mattson type theorems
Authors
Tsuyoshi Miezaki
Akihiro Munemasa
Hiroyuki Nakasora
Publication date
23-02-2021
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 5/2021
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-00848-w

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