Optimized algorithms for binary BCH codes

Although various universal algorithms have been proposed for Key Equation Solver(KES), the most critical part of Reed-Solomon(RS) codes, little optimization has been done for their binary sibling-binary BCH codes. This paper presents two binary versions of reformulated inverse-free Berlekamp-Massey (riBM) algorithm. The proposed algorithms halve iteration cycles and arrange variables more flexibly and effectively. The first simplified algorithm reduces about 1/3 fewer process elements and registers, while the second requires only one half of gate counts compared to the original riBM algorithm. Also folded architectures can be adopted because both of the two optimized algorithms are symmetrical and regular.