On Step-by-Step Complete Decoding Triple-Error-Correcting Binary BCH Codes

The decoding beyond the Bose-Chaudhuri-Hocquenghem (BCH) bound is always an interesting research topic in block error correction codes. However, searching a complete decoding algorithm is not easy since all the error patterns that belong to the coset leaders of the standard array need to be correctable [1]. Both the well-known standard algebraic method and the step-by-step method can be used to decode the binary BCH codes [2], [3]. The major advantage of the step-by-step decoding is that it only needs to know the syndrome difference for different number of errors, without the need to find the complicated error location polynomial [3], [4]. Since the syndrome difference for different number of errors can be extracted from the error location polynomial, a less complex step-by-step complete decoding algorithm can be easily obtained once the standard algebraic method is found, such as the double-error-correcting binary BCH codes [2], [5]. In this paper, according to the properties found in the algebraic complete decoding algorithm of triple-error-correcting binary BCH codes [6], a step-by-step complete decoding algorithm of the codes is introduced.