English

Finding codes on infinite grids automatically

Combinatorics 2026-04-08 v4 Discrete Mathematics Formal Languages and Automata Theory Dynamical Systems

Abstract

We apply automata theory and Karp's minimum mean weight cycle algorithm to minimum density problems in coding theory. Using this method, we find the new upper bound 53/1260.420653/126 \approx 0.4206 for the minimum density of an identifying code on the infinite hexagonal grid, down from the previous record of 3/70.42863/7 \approx 0.4286.

Keywords

Cite

@article{arxiv.2303.00557,
  title  = {Finding codes on infinite grids automatically},
  author = {Ville Salo and Ilkka Törmä},
  journal= {arXiv preprint arXiv:2303.00557},
  year   = {2026}
}

Comments

19 pages, 5 figures

R2 v1 2026-06-28T08:54:19.670Z