New decoder for triple-error-correcting binary BCH codes

Abstract

A step-by-step decoding algorithm is introduced for triple-error correcting binary BCH codes of length n = 2^m -1. The error bit can be directly determined by this algorithm, and the computation is simple and regular. Based on the analysis of the decoding algorithm, the hardware decoder is improved in continuous decoding condition. Furthermore, a new method for the key point of this algorithm, the look-up table of (x₁ ^')⁵ + (x₂ ^')⁵, is presented to simplify the difficult hardware decoder.