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

✍ Scribed by Masaaki Harada; Hadi Kharaghani

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 212 KB
Volume: 13
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20046

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✦ Synopsis

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. © 2005 Wiley Periodicals, Inc. J Combin Designs 13: 184–194, 2005.

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