Defining the $q$-Analogue of a Matroid

  • Relinde Jurrius
  • Ruud Pellikaan
Keywords: Matroid theory, q-Analogue, Rank Metric Codes

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. 

Published
2018-07-13
Article Number
P3.2