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Orthogonal designs, self‐dual codes, and the Leech lattice
Author(s) -
Harada Masaaki,
Kharaghani Hadi
Publication year - 2005
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20046
Subject(s) - mathematics , dual (grammatical number) , orthogonal array , circulant matrix , lattice (music) , hadamard transform , ternary operation , hadamard matrix , combinatorial design , binary number , combinatorics , construct (python library) , discrete mathematics , arithmetic , computer science , physics , art , mathematical analysis , statistics , literature , taguchi methods , acoustics , programming language
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.