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

Masaaki Harada, Hadi Kharaghani

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2005 Dec 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Orthogonal designs, self-dual codes, and the Leech lattice'. Together they form a unique fingerprint.

Cite this