An upper bound on the size of a binary code with $$s$$ distances

Abstract

Let $$C$$ be a binary code of length $$n$$ with distances $$0<d_1<\cdots<d_s\le n$$. In this note we prove a general upper bound on the size of $$C$$ without any restriction on the distances $$d_i$$. The bound is asymptotically optimal.