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- W3021782157 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 that, 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 S(2, 3, 13; q) q-Steiner systems and hence establish the existence of subspace designs with previously unknown parameters." @default.
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- W3021782157 date "2020-05-07" @default.
- W3021782157 modified "2023-09-27" @default.
- W3021782157 title "Constructions of new matroids and designs over GF(q)" @default.
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