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 and steganography. The 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 the 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.
Classification of minimal 1-saturating sets in PG(2,q), q<= 23
BARTOLI, DANIELE;FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2012
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 and steganography. The 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 the 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.File in questo prodotto:
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