On the Limit Distribution of the Distance Between a Random Vector and Some Binary Codes

We obtain theorems on the limit distribution of the Hamming distance between a random vector and some binary codes. We assume that the codes that we consider are distance-invariant; the conditions of the theorems are expressed in terms of the weight (distance) spectrum. The results are applied to obtain a lower bound on the covering radius of a code. As examples, we consider some well-known codes.