engleski

Self-orthogonal Z_{;2^k};-codes constructed from Boolean functions

The subject of this talk is a construction of self-orthogonal codes over Z_{;2^k}; from Boolean functions. First, we give a construction of a self-orthogonal Z4-code of length 2^{;n+1}; from a pair of bent functions on n variables. We prove that for n ≥ 4 those codes can be extended to Type IV-II Z4- codes. From that family of Type IV-II Z4-codes, we construct a family of self-dual Type II binary codes by using the Gray map. We construct a self-orthogonal Z_{;2^k};-code of length 2^{;n+1}; with all Euclidean weights divisible by 2^{;k+2}; from a pair of bent functions on n variables, for every k ≥ 3. Moreover, we give a construction of a self- orthogonal Z_{;2^k};-code of length 2^{;n+2}; with all Euclidean weights divisible by 2^{;k+1}; from a pair of Boolean functions on n variables, for every 3 ≤ k ≤ n.

Boolean function, Type II binary code, Z4-code, self-orthogonal Z_{;2^k};-code

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