English

On $q$-analog Steiner systems of rank metric codes

Combinatorics 2017-09-05 v1

Abstract

In this paper we prove that rank metric codes with special properties imply the existence of qq-analogs of suitable designs. More precisely, we show that the minimum weight vectors of a [2d,d,d][2d,d,d] dually almost MRD code CFqmnC\leq \mathbb{F}_{q^m}^n which has no code words of rank weight d+1d+1 form a qq-analog Steiner system Sq(d1,d,2d)S_q(d-1,d,2d). In particular, d+1d+1 must be a prime.

Keywords

Cite

@article{arxiv.1709.00598,
  title  = {On $q$-analog Steiner systems of rank metric codes},
  author = {F. Arias and J. de la Cruz and J. Rosenthal and W. Willems},
  journal= {arXiv preprint arXiv:1709.00598},
  year   = {2017}
}