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).
Constructions of new matroids and designs over Fq / Byrne, Eimear; Ceria, Michela; Ionica, Sorina; Jurrius, Relinde; Sacikara, Elif. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - STAMPA. - 91:2(2023), pp. 451-473. [10.1007/s10623-022-01087-3]
Constructions of new matroids and designs over Fq
Ceria, Michela;
2023-01-01
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).| File | Dimensione | Formato | |
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