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A new lower bound for the football pool problem for 7 matches. (English) Zbl 0866.94027

Summary: Let \(K_3(7,1)\) denote the minimum cardinality of a ternary code of length 7 and covering radius one. In a previous paper [J. Comb. Theory, Ser. A 67, No. 2, 199-222 (1994; Zbl 0815.94021)], we improved on the lower bound \(K_3(7,1)\geq 147\) by showing that \(K_3(7,1)\geq 150\). In this note, we prove that \(K_3(7,1)\geq 153\).

MSC:

94B65 Bounds on codes
94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory

Citations:

Zbl 0815.94021
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References:

[1] Chen And, W.Honkala, I.S., Lower bounds for q-ary covering codes, IEEE Trans. Inform. Theory36 (1990), 664-671. · Zbl 0703.94014
[2] Cohen, G.D., Litsyn, S.N., Lobstein, A.C. and Mattson, H.F., Covering radius 1985-1994, preprint. · Zbl 0873.94025
[3] Habsieger, L., Lower bounds for q-ary coverings by spheres of radius one, J. Combin. Theory Ser. A 67 (1994), 199-222. · Zbl 0815.94021
[4] Habsieger, L., Binary codes with covering radius one: some new lower bounds, Discrete Mathematics, to appear. · Zbl 0898.94016
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