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Covering radius – survey and recent results. (English) Zbl 0586.94014
All known results on the covering radius are presented, as well as some new results. Lower and upper bounds on covering radius are given in sections II and III, respectively. Section IV gives covering radius results for Reed-Muller codes, and section V deals with the least covering radius of \((n,k)\) codes. In section VI, \(t[n,k]\) is determined for small \(k\). The asymptotic results are presented in section VII, and section VIII provides some additional, miscellaneous results. Finally, in section IX, some open problems are given. In addition, Appendix B provides some codes of known covering radius and a table of the values of \(t[n,k]\) for \(n\leq 32\) and \(k\leq 25\).

MSC:
94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory
94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
94B05 Linear codes (general theory)
11H71 Relations with coding theory
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