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Constructions of new matroids and designs over GF(q) by Byrne, Eimear; Ceria, Michela; Ionica, Sorina; Jurrius, Relinde; Saçikara, Elif is a scholarly article available to read on EtoBox.

What is Constructions of new matroids and designs over GF(q) about?

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).

Author

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

Published

2020

Language

EN