q-Steiner Systems Do Exist
Michael Braun, Alfred Wassermann
TL;DR
This paper presents the first known construction of q-analog Steiner systems, specifically q-Steiner Systems S_2[2,3,13], using computational methods and group automorphisms.
Contribution
It introduces the first explicit construction of q-analog Steiner systems and demonstrates their existence through computational search.
Findings
At least 26 q-Steiner Systems S_2[2,3,13] found
Systems admit the normalizer of a singer cycle as automorphisms
First known construction of q-analog Steiner systems
Abstract
In this paper we give the first construction of a q-analog of a Steiner system. Using a computer search we found at least 26 q-Steiner Systems S_2[2,3,13] admitting the normalizer of a singer cycle as a group of automorphisms.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research