Blind Reconstruction of BCH Codes Based on Consecutive Roots of Generator Polynomials

Abstract

In this letter, a blind reconstruction method of Bose-Chaudhuri-Hocquenghem (BCH) codes is proposed, which uses the property that all the codeword polynomials of a $t$ -error correcting BCH code have the same $2t$ consecutive roots over Galois field. The proposed method inherently eliminates most of the erroneous codewords from the received codewords by utilizing the information about the starting position and length of consecutive roots of each received codeword. Therefore, the blind reconstruction performance is substantially improved and the simulation results confirm that the proposed method outperforms other blind reconstruction methods.