Blind reconstruction of BCH codes based on candidate generator polynomial in random situation

A novel method for blind reconstruction of binary Bose–Chaudhuri–Hocquenghem codes is proposed. Compared to previously reported works, a new approach to find the goal generator polynomial is employed. First, using the feature that each codeword polynomial of a t-error-correcting Bose–Chaudhuri–Hocquenghem code has the same 2t consecutive roots over Galois field, a new set of candidate generator polynomials is introduced. Then, this set in a random situation to find the correct generator polynomial is investigated. Monte Carlo simulations demonstrate the superiority of the proposed reconstruction algorithm compared to the previous methods.