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, Tome 8 (1996) no. 2, pp. 481-484

Abstract (VO)
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 Zbl

DOI : 10.5802/jtnb.183

@article{JTNB_1996__8_2_481_0,
     author = {Laurent Habsieger},
     title = {A new lower bound for the football pool problem for $7$ matches},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {481--484},
     year = {1996},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     doi = {10.5802/jtnb.183},
     zbl = {0866.94027},
     mrnumber = {1438484},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.183/}
}

TY  - JOUR
AU  - Laurent Habsieger
TI  - A new lower bound for the football pool problem for $7$ matches
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1996
SP  - 481
EP  - 484
VL  - 8
IS  - 2
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.183/
DO  - 10.5802/jtnb.183
LA  - en
ID  - JTNB_1996__8_2_481_0
ER  -

%0 Journal Article
%A Laurent Habsieger
%T A new lower bound for the football pool problem for $7$ matches
%J Journal de théorie des nombres de Bordeaux
%D 1996
%P 481-484
%V 8
%N 2
%I Université Bordeaux I
%U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.183/
%R 10.5802/jtnb.183
%G en
%F JTNB_1996__8_2_481_0

Laurent Habsieger. A new lower bound for the football pool problem for $7$ matches. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 481-484. doi: 10.5802/jtnb.183

Bibliographie
Cité par

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

[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 | Zbl

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

Cité par Sources :