Synthesis-by-analysis of BCH Codes

In this paper we propose a technique to blindly synthesize the generator polynomial of BCH codes. The proposed technique involves finding Greatest Common Divisor (GCD) among different codewords and block lengths. Based on this combinatorial GCD calculation, correlation values are found. For a valid block length, the iterative GCD calculation results either into generator polynomial or some of its higher order multiples. These higher order polynomials are factorized under modulo-2 operation, and one of the resulting factors is always the generator polynomial which further increases the correlation value. The resulting correlation plot for different polynomials shows very high values for correct block length and valid generator polynomial. Knowing the valid block length and generator polynomial, all other parameters including number of parity-check digits (n− k), minimum distance dmin and error correcting capability t are readily exposed.