Construction of cocyclic Complex and Butson Hadamard matrices and Simplex codes
by
P. R. Nimalsiri
Department of Mathematics and Statistics, RMIT University, Victoria 3001

Several researchers have studied the use of cocycles to construct Hadamard matrices and subsequently these matrices have been used for the construction of error correcting codes.

In 1962, Butson introduced the Butson Hadamard matrices and in 1970, Turyn introduced the complex Hadamard matrices. Since then several methods have been introduced for the construction of Butson Hadamard matrices and complex Hadamard matrices.

In this talk we define a cocycle over the Galois ring GR(4, m) for the construction of complex Hadamard matrices and a cocycle over the Galois ring GR(2^s, m) for the construction of Butson Hadamard matrices. Then we use the cocyclic complex Hadamard matrices for the construction of simplex codes over the integers modulo 4 and the cocyclic Butson Hadamard matrices for the construction of simplex codes over the integers modulo 2^s.

Date received: September 19, 2003