Abstract
AbstractA 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).
Funder
Swiss Government Excellence Scholarship
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications
Reference29 articles.
1. Aigner M.: Combinatorial Theory. Springer, New York (1979).
2. Bollen G., Crapo H., Jurrius R.: The Tutte $$q$$-Polynomial (2017). arxiv:1707.03459.
3. Braun M.: Some new designs over finite fields. Bayreuth. Math. Schr. 74, 58 (2005).
4. Braun M., Etzion T., Östergård P.R.J., Vardy A., Wassermann A.: Existence of $$q$$-analogs of Steiner systems. Forum Math. Pi 4, e7 (2016). https://doi.org/10.1017/fmp.2016.5.
5. Braun M., Kerber A., Laue R.: Systematic construction of $$q$$-analogs of $$t$$-$$(v, k, \lambda )$$-designs. Des. Codes Cryptogr. 34(1), 55–70 (2005).
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