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

Laurent Habsieger

Journal de théorie des nombres de Bordeaux (1996)

  • Volume: 8, Issue: 2, page 481-484
  • ISSN: 1246-7405

Abstract

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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 ) 147 by showing that K 3 ( 7 , 1 ) 150 . In this note, we prove that K 3 ( 7 , 1 ) 153 .

How to cite

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Habsieger, Laurent. "A new lower bound for the football pool problem for $7$ matches." Journal de théorie des nombres de Bordeaux 8.2 (1996): 481-484. <http://eudml.org/doc/247830>.

@article{Habsieger1996,
abstract = {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 $K_3(7,1) \ge 147$ by showing that $K_3(7,1) \ge 150$. In this note, we prove that $K_3(7,1) \ge 153$.},
author = {Habsieger, Laurent},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {ternary code; covering radius},
language = {eng},
number = {2},
pages = {481-484},
publisher = {Université Bordeaux I},
title = {A new lower bound for the football pool problem for $7$ matches},
url = {http://eudml.org/doc/247830},
volume = {8},
year = {1996},
}

TY - JOUR
AU - Habsieger, Laurent
TI - A new lower bound for the football pool problem for $7$ matches
JO - Journal de théorie des nombres de Bordeaux
PY - 1996
PB - Université Bordeaux I
VL - 8
IS - 2
SP - 481
EP - 484
AB - 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 $K_3(7,1) \ge 147$ by showing that $K_3(7,1) \ge 150$. In this note, we prove that $K_3(7,1) \ge 153$.
LA - eng
KW - ternary code; covering radius
UR - http://eudml.org/doc/247830
ER -

References

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  1. [1] W. Chen And I.S. Honkala, Lower bounds for q-ary covering codes, IEEE Trans. Inform. Theory36 (1990), 664-671. Zbl0703.94014MR1053861
  2. [2] G.D. Cohen, S.N. Litsyn, A.C. Lobstein and H.F. Mattson, Covering radius 1985-1994, preprint. Zbl0873.94025
  3. [3] L. Habsieger, Lower bounds for q-ary coverings by spheres of radius one, J. Combin. Theory Ser. A67 (1994), 199-222. Zbl0815.94021MR1284408
  4. [4] L. Habsieger, Binary codes with covering radius one: some new lower bounds, Discrete Mathematics, to appear. Zbl0898.94016MR1477282

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