engleski

Binary Codes from Skew-symmetric Hadamard Matrices

A Hadamard matrix of order m is a square matrix with entries 1 and -1 such that HHT = m I_m . A Hadamard matrix H of order m is skew- symmetric if H = A + I_m , where A^T = −A. Each Hadamard matrix corresponds to a 2−(m − 1, m/2− 1, m/4− 1) design, called a Hadamard design, and vice versa. A Hadamard 3−design is design with parameters 3 −(m, m/2, m/4− 1) which can be obtained from a Hadamard design and conversely. By its incidence matrix we obtain binary codes of length m. We present a method for obtaining skew-symmetric Hadamard matrices of dimension 4m from skew- symmetric Hadamard matrices of order m. We will consider the case m = 8 and discuss obtained binary codes. This is joint work with Dean Crnkovic and Sanja Rukavin

Skew-symmetric Hadamard matrix, Hadamard design

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