Classification of minimal 1-saturating sets in PG(2,q), q≤ 23

2012/03/06 by Daniele Bartoli, Bartoli, Daniele, Stefano Marcugini +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1203.1133

4 pages

arxiv created 2012/03/06 · arxiv updated 2012/03/07

Abstract

Minimal 1-saturating sets in the projective plane PG(2,q) are considered. They correspond to covering codes which can be applied to many branches of combinatorics and information theory, as data compression, compression with distortion, broadcasting in interconnection network, write-once memory or steganography (see \citeCoh and \citeBF2008). The full classification of all the minimal 1-saturating sets in PG(2,9) and PG(2,11) and the classification of minimal 1-saturating sets of smallest size in PG(2,q), 16≤ q≤ 23 are given. These results have been found using a computer-based exhaustive search that exploits projective equivalence properties.

Related

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• Upper bounds on the smallest size of a saturating set in projective planes and spaces of even dimension