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