Codes From Generalized Hadamard Matrices

The Hadamard Matrices are widely used in communication systems, data compression, error control coding, cryptography, linear filtering and spectral analysis. Such a popularity of Hadamard matrices is explained by their simplicity and efficiency in a variety of concrete practical realizations. In this paper we consider a family {H_m}, m =1,2,.., of generalized Hadamard matrices of order p^m , where p is a prime number, and construct the corresponding family {C^*m} of generalized p-ary Hadamard codes which meet the Plotkin bound.