Geodesic
Defining the \(q\)-analogue of a matroid
Relinde Jurrius1 ; Ruud Pellikaan2
1Netherlands Defence Academy
2Eindhoven University of Technology
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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This paper defines the $q$-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a $q$-matroid, and why they are (not) cryptomorphic. Also, we explain the motivation for studying $q$-matroids by showing that a rank metric code gives a $q$-matroid.
DOI : 10.37236/6569
Classification : 05B35, 05A30
Mots-clés : matroid theory, \(q\)-analogue, rank metric codes

Relinde Jurrius  1   ; Ruud Pellikaan  2

1 Netherlands Defence Academy
2 Eindhoven University of Technology 
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Relinde Jurrius; Ruud Pellikaan. Defining the \(q\)-analogue of a matroid. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/6569

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