Improved lower bound for locating-dominating codes in binary Hamming spaces

: Junnila Ville, Laihonen Tero, Lehtilä Tuomo

Publisher: SPRINGER

: 2022

: Designs, Codes and Cryptography

: DESIGNS CODES AND CRYPTOGRAPHY

: DESIGN CODE CRYPTOGR

: 90

: 67

: 85

: 19

: 0925-1022

: 1573-7586

DOI: https://doi.org/10.1007/s10623-021-00963-8(external)

: https://link.springer.com/article/10.1007/s10623-021-00963-8(external)

: https://arxiv.org/abs/2102.05537(external)

In this article, we study locating-dominating codes in binary Hamming spaces 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. (Discret Math Theor Comput Sci 6(2):265, 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 >= 10. 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.