Self-Dual Codes over Z4 and Unimodular Lattices: A Survey
نویسنده
چکیده
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 world, known families of
منابع مشابه
Double Circulant Codes over <InlineEquation ID="IE1"> <EquationSource Format="MATHTYPE"> <![CDATA[% MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf % gDOjdaryqr1ngBPrginfgDObcv39gaiuaacqWFKeIwdaWgaaWcbaGa % aGinaaqabaaaaa!419E! ]]> </EquationSource> <EquationSource Format="TEX"> <![CDATA[$$\mathbb{Z}_4 $$]]> </EquationSource> </InlineEquation> and Even Unimodular Lattices
With the help of some new results about weight enumerators of self-dual codes overZ4 we investigate a class of double circulant codes over Z4, one of which leads to an extremal even unimodular 40-dimensional lattice. It is conjectured that there should be “Nine more constructions of the Leech lattice”.
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