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)

Research output: Contribution to journal › Article › peer-review

Abstract

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).

Original language	English
Pages (from-to)	365-370
Number of pages	6
Journal	Journal of Combinatorial Theory. Series A
Volume	104
Issue number	2
DOIs	https://doi.org/10.1016/j.jcta.2003.08.004
Publication status	Published - 1 Jan 2003

Keywords

Covering code
Group of automorphisms
Simulated annealing

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10.1016/j.jcta.2003.08.004

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KW - Group of automorphisms

KW - Simulated annealing

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JF - Journal of Combinatorial Theory. Series A

IS - 2

ER -

K₅(7,3) ≤ 100

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Keywords

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