English

Rank-metric codes, linear sets, and their duality

Combinatorics 2018-06-18 v1

Abstract

In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of [18, Section 5] on linear sets on a projective line. We extend this to linear sets in arbitrary dimension, giving the connection between two constructions for linear sets defined in [9]. Finally, we then exploit this connection by using the MacWilliams identities to obtain information about the possible weight distribution of a linear set of rank n on a projective line PG(1,qn)PG(1, q^n).

Keywords

Cite

@article{arxiv.1806.05929,
  title  = {Rank-metric codes, linear sets, and their duality},
  author = {John Sheekey and Geertrui Van de Voorde},
  journal= {arXiv preprint arXiv:1806.05929},
  year   = {2018}
}
R2 v1 2026-06-23T02:31:11.402Z