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

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^λ) 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.