VLSI Architectures for Modern Error-Correcting Codes

3

Root computations for polynomials over finite fields

CONTENTS

3.1 Root computation for general polynomials

3.2 Root computation for linearized and affine polynomials

3.3 Root computation for polynomials of degree two or three

Root computations for polynomials over finite fields are needed in Reed-Solomon and Bose-Chaudhuri-Hocquenghem (BCH) decoding algorithms. This chapter presents methods and implementation architectures for such root computations.

3.1 Root computation for general polynomials

The roots of a general polynomial over finite fields are computed by exhaustive Chien search, which tests each finite field element to see if it is a root. Efficient Chien search architectures can be found in many papers, such as [29].

Fig. 3.1 ...