Self-orthogonal 3-(56,12,65) designs and extremal doubly-even self-dual codes of length 56

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Abstract

In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65) design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic self-orthogonal 3-(56,12,65) designs.

Original languageEnglish
Pages (from-to)5-16
Number of pages12
JournalDesigns, Codes, and Cryptography
Volume38
Issue number1
DOIs
Publication statusPublished - 2006 Jan 1
Externally publishedYes

Keywords

  • Extremal doubly-even self-dual code
  • Self-orthogonal design

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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