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Improved Lower Bound for Locating-Dominating Codes in Binary Hamming Spaces

Ville Junnila 1 Tero Laihonen 1 Tuomo Lehtilä 1, 2 
2 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : In this article, we study locating-dominating codes in binary Hamming spaces $\mathbb{F}^n$. Locating-dominating codes have been widely studied since their introduction in 1980s by Slater and Rall. They are dominating sets suitable for distinguishing vertices in graphs. Dominating sets as well as locating-dominating codes have been studied in Hamming spaces in multiple articles. Previously, Honkala et al. (2004) have presented a lower bound for locating-dominating codes in binary Hamming spaces. In this article, we improve the lower bound for all values $n\geq10$. In particular, when $n=11$, we manage to improve the previous lower bound from $309$ to $317$. This value is very close to the current best known upper bound of $320$.
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https://hal.archives-ouvertes.fr/hal-03386094
Contributor : Tuomo Lehtilä Connect in order to contact the contributor
Submitted on : Tuesday, October 19, 2021 - 5:13:07 PM
Last modification on : Friday, September 30, 2022 - 11:34:16 AM

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Ville Junnila, Tero Laihonen, Tuomo Lehtilä. Improved Lower Bound for Locating-Dominating Codes in Binary Hamming Spaces. Designs, Codes and Cryptography, 2021, ⟨10.1007/s10623-021-00963-8⟩. ⟨hal-03386094⟩

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