A new lower bound for the football pool problem for $7$ matches

Laurent Habsieger

doi:10.5802/jtnb.183

A new lower bound for the football pool problem for

7

matches

Laurent Habsieger

Journal de Théorie des Nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 481-484.

Abstract
Résumé

Let $K_{3} (7, 1)$ denote the minimum cardinality of a ternary code of length $7$ and covering radius one. In a previous paper, 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 $K_{3} (7, 1) \geq 153$ .

Notons $K_{3} (7, 1)$ le cardinal minimal d’un code ternaire de longueur $7$ et de rayon de recouvrement un. Dans un précédent article, nous avons amélioré la minoration $K_{3} (7, 1) \geq 147$ en montrant que $K_{3} (7, 1) \geq 150$ . Dans cette note, nous prouvons que $K_{3} (7, 1) \geq 153$ .

MR: 1438484 | Zbl: 0866.94027

DOI: 10.5802/jtnb.183

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     title = {A new lower bound for the football pool problem for $7$ matches},
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     pages = {481--484},
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Laurent Habsieger. A new lower bound for the football pool problem for $7$ matches. Journal de Théorie des Nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 481-484. doi : 10.5802/jtnb.183. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.183/

References
Cited by

[1] W. Chen And I.S. Honkala, Lower bounds for q-ary covering codes, IEEE Trans. Inform. Theory 36 (1990), 664-671. | MR: 1053861 | Zbl: 0703.94014

[2] G.D. Cohen, S.N. Litsyn, A.C. Lobstein and H.F. Mattson, Covering radius 1985-1994, preprint.

[3] L. Habsieger, Lower bounds for q-ary coverings by spheres of radius one, J. Combin. Theory Ser. A 67 (1994), 199-222. | MR: 1284408 | Zbl: 0815.94021

[4] L. Habsieger, Binary codes with covering radius one: some new lower bounds, Discrete Mathematics, to appear. | MR: 1477282 | Zbl: 0898.94016

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