Title: A selection of divisible lexicographic codes

Authors: Harold N. Ward

Addresses: Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA

Abstract: This paper presents a selection of lexicographic codes over a prime field Fp, 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!

Keywords: lexicographic codes; divisible codes; quadratic residues; spread; translation plane; Hall plane; Griesmer bound; Vera Pless.

DOI: 10.1504/IJICOT.2010.032866

International Journal of Information and Coding Theory, 2010 Vol.1 No.4, pp.410 - 428

Published online: 25 Apr 2010 *

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