engleski

New extremal Type II Z_4-codes of length 32 obtained from Hadamard designs

The subject of this talk is a construction of new extremal Type II Z_4-codes of length 32 from Hadamard designs. For every Hadamard design with parameters 2-(n-1, n/2-1, n/4-1) having a skew-symmetric incidence matrix we give a construction of 54 Hadamard designs with parameters 2-(4n-1, 2n-1, n-1). Moreover, for the case n = 8 we construct doubly-even self-orthogonal binary linear codes from the corresponding Hadamard matrices of order 32. From these binary codes we construct 5 new extremal Type II Z_4-codes of length 32. The constructed codes are the first examples of extremal Type II Z_4-codes of length 32 and type 4^{;k_1};2^{;k_2};, k_1\in {;7, 8, 9, 10};, whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II Z_4-codes of length 32 and type 4^{;14};2^{;4};. This is a joint work with Dean Crnkovic, Matteo Mravic and Sanja Rukavina.

Type II Z_4-codes ; Hadamard designs ; doubly-even binary codes

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