EXACT MINIMUM DENSITY OF CODES IDENTIFYING VERTICES IN THE SQUARE GRID

摘要

An identifying code C is a subset of the vertices of the square grid Z~2 with the property that for each element υ of Z~2, the collection of elements from Cat a distance of at most one from υ is nonempty and distinct from the collection of any other vertex. We prove that the minimum density of C within Z~2 is 7/(20).