engleski

New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices

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 five 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^k1 2^k2 , k1 ∈ {; ; ; 7, 8, 9, 10}; ; ; , whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II Z4 -codes of length 32 and type 4^14 2^4.

Hadamard matrix ; Z4 -code ; extremal Type II Z4 -code

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