A geometric approach to generalized covering radii of linear codes (opens in new tab)

Covering problems in coding theory are closely related to finite geometry through the interpretation of the columns of parity-check matrices as point sets in finite vector spaces. Motivated by the recent notion of generalized covering radii of linear codes introduced by Elimelech, Firer and Schwartz, we develop a geometric framework for these parameters. We introduce $(\rho,t)$-saturating sets and show that they are precisely the finite-geomet...