Kolev, Emil; Hill, Ray An improved lower bound on the covering number \(K_2(9,1)\). (English) Zbl 0933.94039 Discrete Math. 197-198, 483-489 (1999). Here the authors improve the lower bound for \(K_2(9,1)\), the minimum cardinality of a binary code of length 9 and covering radius 1 in showing that a binary code of length 9, 55 codewords and covering radius 1 does not exist giving the new lower bound \(K_2(9,1)\geq 56\). In a later paper they obtain the bound 57 (see the following review Zbl 0933.94040). The best upper bound \(K(9)\leq 62\) has been obtained by L. T. Wille. Reviewer: Olaf Ninnemann (Uffing am Staffelsee) Cited in 1 Review MSC: 94B65 Bounds on codes 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory 94B60 Other types of codes Keywords:minimum cardinality; binary code; covering radius Citations:Zbl 0933.94040 PDFBibTeX XMLCite \textit{E. Kolev} and \textit{R. Hill}, Discrete Math. 197--198, 483--489 (1999; Zbl 0933.94039) Full Text: DOI References: [1] Cohen, G. D.; Litsyn, S. N.; Lobstein, A. C.; Mattson, H. F., Covering Radius 1985-1994, Appl. Algebra Eng. Commun. Comput., 8, 3, 173-239 (1997) · Zbl 0873.94025 [2] Wille, L. T., Improved binary code coverings by simulated annealing, (Congr. Numer., 73 (1990)), 53-58 [3] Wille, L. T., New binary covering codes obtained by simulated annealing, IEEE Trans. Inform. Theory, 42, 300-302 (1996) · Zbl 0851.94031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.