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, E.; Ceria, M.; Ionica, S.; Jurrius, R.; Sacikara, E.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 91:2(2023), pp. 451-473. [10.1007/s10623-022-01087-3]

Constructions of new matroids and designs over Fq

Ceria M.;
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).
2023
Constructions of new matroids and designs over Fq / Byrne, E.; Ceria, M.; Ionica, S.; Jurrius, R.; Sacikara, E.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 91:2(2023), pp. 451-473. [10.1007/s10623-022-01087-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/250840
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