A Fast and Efficient Two-Dimensional Chien Search Algorithm and Design Architecture

Abstract

We develop an efficient procedure for finding the roots of a bi-variate polynomial over $GF(q)$ by extending the Chien search procedure to two-dimensions. The complexity of the Chien search is further reduced to an order of the number of conjugacy classes over $GF(q^{\lambda })$ leading to a significant reduction in the computational complexity. We also provide an efficient design architecture for our algorithm towards a circuit realization that produces the roots in ‘1’ clock cycle.