Blind Reconstruction of Binary Cyclic Codes

In this paper, we consider the problem of blind reconstruction of binary cyclic codes from a received sequence of noise affected codewords. Blind reconstruction of a cyclic code is equivalent to identifying its generator polynomial. We identify the generator polynomial by finding its irreducible factors and their respective multiplicities. We derive syndrome distributions of the received vectors when the divisor polynomial is a factor of the generator polynomial and when it is not a factor. These distributions are used to construct a Neyman-Pearson hypothesis test to distinguish between factors and non-factors of the generator polynomial.