Orthogonal designs, self-dual codes, and the Leech lattice

Masaaki Harada, Hadi Kharaghani

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Symmetric designs and Hadamard matrices are used to construct binary and ternary self-dual codes. Orthogonal designs are shown to be useful in construction of self-dual codes over large fields. In this paper, we first introduce a new array of order 12, which is suitable for any set of four amicable circulant matrices. We apply some orthogonal designs of order 12 to construct new self-dual codes over large finite fields, which lead us to the odd Leech lattice by Construction A.

Original languageEnglish
Pages (from-to)184-194
Number of pages11
JournalJournal of Combinatorial Designs
Volume13
Issue number3
DOIs
Publication statusPublished - 2005 Dec 1
Externally publishedYes

Keywords

  • Orthogonal design
  • Self-dual code
  • The Leech lattice

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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