This paper contributes to the study of rank-metric codes from an algebraic and combinatorial point of view. We introduce q-polymatroids, the q-analogue of polymatroids, and develop their basic properties. We associate a pair of q-polymatroids with a rank-metric code and show that several invariants and structural properties of the code, such as generalized weights, the property of being MRD or an optimal anticode, and duality, are captured by the associated combinatorial object.
|Number of pages||19|
|Journal||Journal of Algebraic Combinatorics|
|Publication status||Published - 1 Aug 2020|
- Generalized weights
- MRD code
- Optimal anticode
- Rank-metric code