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
نویسنده
چکیده
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”.
منابع مشابه
Derangements and Tensor Powers of Adjoint Modules for <InlineEquation ID="IE1"> <EquationSource Format="MATHTYPE"> <![CDATA[% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xc8Zjab-vc8Snaa% BaaaleaacaWGUbaabeaaaaa!45E7!]]> </EquationSource> <EquationSource Format="TEX"> <![CDATA[$$\mathfrak{s}\mathfrak{l}_n $$]]> </EquationSource> </InlineEquation>
We obtain the decomposition of the tensor spacesl⊗k n as a module forsln , find an explicit formula for the multiplicities of its irreducible summands, and (when n ≥ 2k) describe the centralizer algebra C = Endsln (sl⊗k n ) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of C is given by the number...
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