A selection of divisible lexicographic codes

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, I promised her a paper on the subject – and here it is, at last!