English

Matroids and Codes with the Rank Metric

Combinatorics 2018-03-19 v1

Abstract

We study the relationship between a q-analogue of matroids and linear codes with the rank metric in the vector space of matrices with entries in a finite field. We prove a Greene type identity for the rank generating function of these matroidal structures and the rank weight enumerator of these linear codes. As an application, we give a combinatorial proof of a MacWilliams type identity for Delsarte rank-metric codes.

Keywords

Cite

@article{arxiv.1803.06041,
  title  = {Matroids and Codes with the Rank Metric},
  author = {Keisuke Shiromoto},
  journal= {arXiv preprint arXiv:1803.06041},
  year   = {2018}
}

Comments

16 pages

R2 v1 2026-06-23T00:54:59.152Z