Recurrent algorithm for calculation of value of formal derivative of polynomial over Galois field and its hardware implementation

Abstract

Within the scope of this scientific paper the formal derivative of the polynomial over the Galois field GF(pm) and a formula for calculation of the formal derivative are considered. Calculation of the formal derivative of the polynomial is used in the decoding algorithm of the information frames during application of the Reed-Solomon codes, which are widely used in the data transmission and storage systems with the data redundancy. The definition of the formal derivative of polynomial over the Galois field GF(pm) and the recurrent algorithm offered by the author for calculation of the value of the formal derivative of the polynomial over the Galois field GF(pm) with a given argument are also presented. Finally, the hardware implementation of the offered calculation scheme for the case of binary Galois field GF(2m) is also given.