A selection of divisible lexicographic codes. (26th April 2010)

• Record Type: Journal Article
• Authors: Ward, Harold N.
• Is Part Of: International journal of information and coding theory. Volume 1:Number 4(2010)
• Page Start: 410
• Page End: 428
• Publication Date: 2010-04-26
• Subjects: lexicographic codes -- divisible codes -- quadratic residues -- spread -- translation plane -- Hall plane -- Griesmer bound -- Vera Pless; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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!