2020/05/07 by Eimear Byrne, Michela Ceria, Byrne, Eimear +7
Computer Science · Engineering · #05B35 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2005.03369
openalex publication_date 2020/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).