Constructions of new matroids and designs over GF(q)
Combinatorics
2022-09-07 v4
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
Cite
@article{arxiv.2005.03369,
title = {Constructions of new matroids and designs over GF(q)},
author = {Eimear Byrne and Michela Ceria and Sorina Ionica and Relinde Jurrius and Elif Saçikara},
journal= {arXiv preprint arXiv:2005.03369},
year = {2022}
}