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Designs, Codes and Cryptography

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23.02.2021

A note on Assmus–Mattson type theorems

verfasst von: Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

Erschienen in: Designs, Codes and Cryptography | Ausgabe 5/2021

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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.

Vorheriger Artikel New families of self-dual codes

Nächster Artikel On the Resilience of Even-Mansour to Invariant Permutations

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Titel: A note on Assmus–Mattson type theorems
verfasst von: Tsuyoshi Miezaki
Akihiro Munemasa
Hiroyuki Nakasora
Publikationsdatum: 23.02.2021
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 5/2021
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-021-00848-w

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