On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

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Abstract

By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even self-dual code of length 24m for (Formula presented) and (Formula presented.), then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight 4k.

Original languageEnglish
Pages (from-to)373-384
Number of pages12
JournalDesigns, Codes, and Cryptography
Volume76
Issue number3
DOIs
Publication statusPublished - 2015 Sep 6

Keywords

  • Extremal doubly even Self-dual code
  • Self-orthogonal (Formula presented.)-design
  • Weight enumerator

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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