A lower bound on the probability of decoding error over a BSC channel

For a code C of length n and size |C, we estimate the error probability of the maximum likelihood decoding. In this paper we address this problem for the binary symmetric channel (BSC) defined by its transition probability p. We discuss the case when we know the distance distribution of the code. We also assume that the code is regular in the sense that the distribution of the distances from a codeword to other codewords does not depend on the choice of the initial codeword.