engleski

Hadamard matrices and Z4-linear codes

A Z4-linear code of length n is a Z4 sub-module of Z4^n. In the Pless-Leon-Fields article "All Z4 codes of Type II and length 16 are known" a method for construction of self-dual Z4-linear codes is presented. The starting point of this construction is a doubly-even self orthogonal binary code. It is known that binary linear codes obtained from Hadamard 3 designs satisfy these conditions. In this talk I will present a method for obtaining binary codes from Hadamard 3-designs of length 4n starting from skew-symmetric Hadamard matrices of order n. Also I will present some Z4-linear codes that we obtained so far and some partial results. This is joint work with Dean Crnković and Sanja Rukavina.

Binary linear code ; Z4-linear code ; extremal Z4-linear code ; self-dual code ; Hadamard matrix ; Skew-symmetric Hadamard matrix ; Hadamard design

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