A selection of divisible lexicographic codes

摘要

This paper presents a selection of lexicographic codes over a prime field F_p, codes constructed so as to be linear and to have a prescribed minimum distance and divisor. The development of the code when the minimum distance is 3p and the divisor is p leads to questions involving the distribution of quadratic residues and non-residues modulo p. In the course of events, the Hall plane H(p) emerges. This paper is dedicated to Vera Pless on the occasion of her retirement. She was in the audience when I presented a sketchy version of the material at a conference at Lehigh University many years ago. In my enthusiasm, 1 promised her a paper on the subject - and here it is, at last!