Blind Detection of BCH Length from Noisy Received Vectors

In this paper, the goal is the length detection of BCH codes from noisy vectors received through a Binary Symmetric Channel (BSC) with cross over probability τ. The proposed method seeks to recover the length of code based on linear properties of cyclic codes. The received bitstream is divided into different likely lengths, and the algorithm puts the divided vector and its shifts in distinct rows of a matrix A. The rank of Λ is calculated, and detector makes a decision based on the rank value, while the rank of the matrix which contains codewords cannot exceed the length of message k /. Therefore, minimum rank is chosen as a sign of linear properties and codewords space. The operation is practical because of the low complexity of calculating the rank, and it can be done over GF(2) and modulo 2 addition.