Constructions of new matroids and designs over GF(q)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2020Embargo end date: 01 Jan 2020Publisher:arXivFunded by:SNSF | New Constructions of Conv...

Authors: Byrne, Eimear; Ceria, Michela; Ionica, Sorina; Jurrius, Relinde; Saçikara, Elif;

doi: 10.48550/arxiv.2005.03369

arXiv: 2005.03369

Constructions of new matroids and designs over GF(q)

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Abstract

A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the q-analogue of a PMD and its properties. In order to do so, we first establish a new cryptomorphic definition for q-matroids. We show that q-Steiner systems are examples of q-PMD's and we use this q-matroid structure to construct subspace designs from q-Steiner systems. We apply this construction to the only known q-Steiner system, which has parameters S(2,3,13;2), and hence establish the existence of a new subspace design with parameters 2-(13,4,5115;2).

Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05B35

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