Finding codes on infinite grids automatically

Published 1 Mar 2023 in math.CO, cs.DM, cs.FL, and math.DS | (2303.00557v4)

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 $53/126 \approx 0.4206$ for the minimum density of an identifying code on the infinite hexagonal grid, down from the previous record of $3/7 \approx 0.4286$.

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