Development of specialized algorithm and hardware implementation for calculation of value of truncated convolution of polynomials over Galois field

Abstract

This scientific paper deals with an algorithm for calculation of the truncated convolution of polynomials over the Galois field GF(pm). Calculation of the truncated convolution of polynomials is a key part of the information frame decoding algorithm on application of the Reed-Solomon codes in the noise protected data transmission and storage systems. Within the scientific paper, the definitions of polynomial and truncated convolution of the polynomials over the Galois field GF(pm) are also overviewed. Finally, the author offers a specialized algorithm for calculation of the value of the truncated convolution of polynomials over the Galois Field GF(pm) with a given argument. Its hardware implementation for the binary Galois field GF(2m) is also presented.