A note on the Assmus–Mattson theorem for some binary codes

Tsuyoshi Miezaki, Hiroyuki Nakasora*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We previously proposed the first nontrivial examples of a code having support t-designs for all weights obtained from the Assmus–Mattson theorem and having support t-designs for some weights with some t> t. This suggests the possibility of generalizing the Assmus–Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening of the Assmus–Mattson theorem along this direction. As a corollary, we provide a new characterization of the extended Golay code G24.

Original languageEnglish
Pages (from-to)1485-1502
Number of pages18
JournalDesigns, Codes, and Cryptography
Volume90
Issue number6
DOIs
Publication statusPublished - 2022 Jun

Keywords

  • Assmus–Mattson theorem
  • Harmonic weight enumerator
  • t-design

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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