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Orthogonal designs, self-dual codes, and the Leech lattice. (English) Zbl 1088.94027
The authors give a construction of an orthogonal matrix of order \(12n\). They use this array to construct orthogonal designs which in turn produce self-dual codes over finite fields of odd order. Following a suggestion of Ozeki, they use these self-dual codes to construct, via construction A, the odd Leech lattice. Self-dual codes that produce this lattice are given for a variety of primes less than 100.

MSC:
94B25 Combinatorial codes
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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