Covering radius---Survey and recent results

Abstract

All known results on covering radius are presented, as well as some new results. There are a number of upper and lower bounds, including asymptotic results, a few exact determinations of covering radius, some extensive relations with other aspects of coding theory through the Reed-Muller codes, and new results on the least covering radius of any linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[n,k]</tex> code. There is also a recent result on the complexity of computing the covering radius.