An upper bound for the minimum weight of the dual codes of desarguesian planes

V. C. Mavron, Thomas McDonough, Jennifer D. Key

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
161 Downloads (Pure)

Abstract

We show that a construction described in [K.L. Clark, J.D. Key, M.J. de Resmini, Dual codes of translation planes, European J. Combinatorics 23 (2002) 529–538] of small-weight words in the dual codes of finite translation planes can be extended so that it applies to projective and affine desarguesian planes of any order p^m where p is a prime, and m≥1. This gives words of weight 2p^m+1-(p^m-1)/(p-1) in the dual of the p-ary code of the desarguesian plane of order p^m, and provides an improved upper bound for the minimum weight of the dual code. The same will apply to a class of translation planes that this construction leads to; these belong to the class of André planes. We also found by computer search a word of weight 36 in the dual binary code of the desarguesian plane of order 32, thus extending a result of Korchmáros and Mazzocca [Gábor Korchmáros, Francesco Mazzocca, On (q+t)-arcs of type (0,2,t) in a desarguesian plane of order q, Math. Proc. Cambridge Phil. Soc. 108 (1990) 445–459].
Original languageEnglish
Pages (from-to)220-229
Number of pages10
JournalEuropean Journal of Combinatorics
Volume30
Issue number1
DOIs
Publication statusPublished - Jan 2009

Fingerprint

Dive into the research topics of 'An upper bound for the minimum weight of the dual codes of desarguesian planes'. Together they form a unique fingerprint.

Cite this