Defining the $q$-Analogue of a Matroid

Relinde Jurrius, Ruud Pellikaan

Abstract


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. 


Keywords


Matroid theory; q-Analogue; Rank Metric Codes

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