On the minimum average distance of binary constant weight codes

Let β(n,M,w) denote the minimum average Hamming distance of a binary constant weight code with length n, size M and weight w. In this paper, we study the problem of determining β(n,M,w). Using the methods from coding theory and linear programming, we derive several lower bounds on the average Hamming distance of a binary constant weight code. These lower bounds enable us to determine the exact value for β(n,M,w) in several cases.