The hybrid method for finding the roots of a polynomial over finite fields based on affine expansion

Abstract

This paper proposes a hybrid method to find the roots of a polynomial in a finite field based on combining the polynomial decomposition into the sum of multiples of the affine polynomial with the analytical method to find the roots of low-order polynomials. The proposed method allows a significant reduction in complexity and is applicable in the design of low-latency BCH and Reed-Solomon decoders.