The Hamming distance between two n-tuples is the number of positions in which they differ. Computing the Hamming distance for a large number of pairs of words is a hard problem. It is important in coding theory since the minimum distance of a code determines the error-correcting capacity of the code. It also has many applications in cryptography.

This paper proposes a method for calculating the Hamming distance for a large number of pairs of words, stored in the form of q-ary integers. The method leads to a problem on intersecting sets, which leads to links with Hadamard designs and symmetric block designs. As a practical application, the proposed method was used for computing the covering radii of a large number of codes.

The description of the method for computing the Hamming distance for a large number of pairs of words leads to links with set theory, extending the interest of the paper beyond coding theory.