Cohen, Gérard D.; Karpovsky, Mark G.; Mattson, H. F. jun.; Schatz, James R. Covering radius – survey and recent results. (English) Zbl 0586.94014 IEEE Trans. Inf. Theory 31, 328-343 (1985). 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 \(k\leq 25\). Reviewer: Shenquan Xie (Xiangtan) Cited in 3 ReviewsCited in 72 Documents 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 Keywords:lower bounds; Hamming distance; translate leader; packing radius; upper bounds; Reed-Muller codes; asymptotic results PDFBibTeX XMLCite \textit{G. D. Cohen} et al., IEEE Trans. Inf. Theory 31, 328--343 (1985; Zbl 0586.94014) Full Text: DOI