Classification of minimal 1-saturating sets in PG(v, 2), 2 <= v <= 6
Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
TL;DR
This paper classifies all minimal 1-saturating sets in projective spaces PG(v, 2) for 2 <= v <= 6, using exhaustive computer search to identify smallest and second smallest sets.
Contribution
It provides a comprehensive classification of minimal 1-saturating sets in PG(v, 2) for v up to 6, including the smallest sets, advancing combinatorial geometry knowledge.
Findings
Complete classification for 2 <= v <= 5
Smallest and second smallest sets in PG(6, 2) identified
Results obtained through exhaustive computer search
Abstract
The classification of all the minimal 1-saturating sets in PG(v, 2) for 2 <= v <= 5, and the classification of the smallest and of the second smallest minimal 1-saturating sets in PG(6, 2) are presented. These results have been found using a computer-based exhaustive search.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research