Universal codes and unimodular lattices
نویسندگان
چکیده
منابع مشابه
Universal codes and unimodular lattices
Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4. We prove in a direct way the equivalence of these two constructions for p ~ 31. In dimension 32, we obtain an extremal lattice of type II not isometric...
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In this paper, we study self-dual codes over the ring Z 2k of the integers modulo 2k with relationships to even unimodular lattices, modular forms, and invariant rings of 1 nite groups. We introduce Type II codes over Z 2k which are closely related to even unimodular lattices, as a remarkable class of self-dual codes and a generalization of binary Type II codes. A construction of even unimodula...
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By using Construction A modulo 4 the following remarkable unimodular lattices have been constructed: the Gosset lattice E8, the Leech lattice, the 23 Niemeier lattices in dimension 24, the two extremal even unimodular lattices in dimension 32 with an automorphism of order 31, all the extremal unimodular lattices and the odd Leech lattice. In this survey, we review basic facts of life in the Z4 ...
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For each prime l with l ≡ 7 (mod 8), we define an action of the ring O = Z[ 2(1 + √ −l)] on the unimodular lattice D l+1 using a Paley matrix. We determine the isomorphism class of D l+1 as an O-module. In particular we show that unless l = 7, D l+1 is not a free O-module. We note a consequence for the Leech lattice.
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 1996
ISSN: 1246-7405
DOI: 10.5802/jtnb.174