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An improved lower bound on the covering number \(K_2(9,1)\). (English) Zbl 0933.94039

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.

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

Citations:

Zbl 0933.94040
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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
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