An Explication of Optimal Equidistant Codes

Abstract

We discuss the problem of characterizing equidistant binary codes of a given length $n$ having largest possible distance and the maximum number of codewords. Such characterizations have been studied by several authors over the years and they involve symmetric BIBDs with certain parameters. In this primarily expository paper, we investigate the history of this problem and give a unified presentation of the main results. Perhaps surprisingly, researchers on this problem were unaware of early relevant work by Marrero and Butson from 1973. Also, it turns out that published results on characterizations of equidistant binary codes have missed one of the possible subcases when $n \equiv 2 \bmod 4$.