K5(7,3) ≤ 100

Guillaume Gommard; Alain Plagne

doi:10.1016/j.jcta.2003.08.004

K₅(7,3) ≤ 100

Guillaume Gommard
, Alain Plagne

Laboratoire d'Informatique (LIX)

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

One of the main aims in the theory of covering codes is to obtain good estimates on K_q (n, R), the minimal cardinality of an R-covering code over the nth power of an alphabet with q elements. This paper reports on the new bound K₅ (7, 3) ≤ 100, obtained by an improved computer search based on Östergård and Weakley's method. In particular, the code leading to this bound has a group of automorphisms. quite different from the one Östergård and Weakley used. This new upper bound significantly improves the former record (which was 125).

langue originale	Anglais
Pages (de - à)	365-370
Nombre de pages	6
journal	Journal of Combinatorial Theory. Series A
Volume	104
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/j.jcta.2003.08.004
état	Publié - 1 janv. 2003

Accès au document

10.1016/j.jcta.2003.08.004

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

@article{cfa903687eb04016953819a5dc4dde3d,

title = "K5(7,3) ≤ 100",

abstract = "One of the main aims in the theory of covering codes is to obtain good estimates on Kq (n, R), the minimal cardinality of an R-covering code over the nth power of an alphabet with q elements. This paper reports on the new bound K5 (7, 3) ≤ 100, obtained by an improved computer search based on {\"O}sterg{\aa}rd and Weakley's method. In particular, the code leading to this bound has a group of automorphisms. quite different from the one {\"O}sterg{\aa}rd and Weakley used. This new upper bound significantly improves the former record (which was 125).",

keywords = "Covering code, Group of automorphisms, Simulated annealing",

author = "Guillaume Gommard and Alain Plagne",

year = "2003",

month = jan,

day = "1",

doi = "10.1016/j.jcta.2003.08.004",

language = "English",

volume = "104",

pages = "365--370",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

number = "2",

}

TY - JOUR

T1 - K5(7,3) ≤ 100

AU - Gommard, Guillaume

AU - Plagne, Alain

PY - 2003/1/1

Y1 - 2003/1/1

N2 - One of the main aims in the theory of covering codes is to obtain good estimates on Kq (n, R), the minimal cardinality of an R-covering code over the nth power of an alphabet with q elements. This paper reports on the new bound K5 (7, 3) ≤ 100, obtained by an improved computer search based on Östergård and Weakley's method. In particular, the code leading to this bound has a group of automorphisms. quite different from the one Östergård and Weakley used. This new upper bound significantly improves the former record (which was 125).

AB - One of the main aims in the theory of covering codes is to obtain good estimates on Kq (n, R), the minimal cardinality of an R-covering code over the nth power of an alphabet with q elements. This paper reports on the new bound K5 (7, 3) ≤ 100, obtained by an improved computer search based on Östergård and Weakley's method. In particular, the code leading to this bound has a group of automorphisms. quite different from the one Östergård and Weakley used. This new upper bound significantly improves the former record (which was 125).

KW - Covering code

KW - Group of automorphisms

KW - Simulated annealing

UR - https://www.scopus.com/pages/publications/0346273076

U2 - 10.1016/j.jcta.2003.08.004

DO - 10.1016/j.jcta.2003.08.004

M3 - Article

AN - SCOPUS:0346273076

SN - 0097-3165

VL - 104

SP - 365

EP - 370

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 2