English

The covering radius of $\mathrm{PGL}_2(q)$

Combinatorics 2017-06-05 v2

Abstract

The covering radius of a subset CC of the symmetric group Sn\mathrm{S}_n is the maximal Hamming distance of an element of Sn\mathrm{S}_n from CC. This note determines the covering radii of the finite projective general linear groups. It turns out that the covering radius of PGL2(q)\mathrm{PGL}_2(q) is q2q-2 if qq is even, and is q3q-3 if qq is odd.

Keywords

Cite

@article{arxiv.1702.04559,
  title  = {The covering radius of $\mathrm{PGL}_2(q)$},
  author = {Binzhou Xia},
  journal= {arXiv preprint arXiv:1702.04559},
  year   = {2017}
}