Generating constant weight binary codes

Abstract

The determination of bounds for A(n, d, w), the maximum possible number of binary vectors of length n, weight w, and pairwise Hamming distance no less than d, is a classic problem in coding theory. Such sets of vectors have many applications. A description is given of how the problem can be used in a first-year undergraduate computational mathematics class as a challenging alternative to more traditional problems, and thus provide motivation for programming with loops and arrays, and the investigation of computational efficiency. Some new results, obtained by a fast implementation of a lexicographic approach, are also presented.