Weight Enuemrtors of Codes over Z/2kZ
نویسنده
چکیده
C is self-dual if C = C⊥. We define a Type II code over R as a self-dual code with Eudidean weights divisible by 4k. We consider the natural projection ρ from Z to R, then this map induces the map (also we denote ρ ) from Zn to Rn. We set Λ(C) = 1 √ 2k ρ−1(C). Theorem 1 If C is self-duel code of length n over R, then the lattice Λ(C) is an n-dimensioal unimodular lattice. Moreover if C is Type II, then the lattice Λ(C) is an even unimodular lattice. Proposition 2 There exists a Type II code of length n over R if and only if n is a multiple of eight. Remark 3 For k = 2, Type II codes of lengths 8 and 16 are classified.
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