engleski

Extremal Type II Z_4-codes from some 2-(31, 15, 7) designs

The subject of this talk is the construction of extremal Type II Z_4−codes from some 2−(31, 15, 7) designs. A symmetric design with parameters (4k−1, 2k−1, k−1) is called a Hadamard 2−design. From this design we can construct a 3−design D* with parameters (4k, 2k, k−1). We consider a binary code spanned by the rows of the block- by-point incidence matrix of D*. For an even k, we proved that such codes are doubly-even binary codes of length 4k, so they can be used to construct self-dual Z_4−codes of length 4k. We got 21 non-equivalent doubly-even binary codes of length 32 from Hadamard 2−designs with parameters (31, 15, 7). We obtained some new extremal Type II Z_4−codes of length 32 from these binary codes. We used some known methods and some improved methods to get new extremal Type II Z_4−codes of lengths 32 and 40 from obtained extremal Type II Z_4−codes of length 32. This is a joint work with Dean Crnković, Matteo Mravić and Sanja Rukavina.

Hadamard 2-design ; Hadamard 3-design ; binary doubly-even code ; Z_4-code ; Euclidean weight ; extremal Type II Z_4-code

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