On identifying codes in the hexagonal mesh

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Abstract

It is shown that, if r⩾2, there exists an (r,⩽2)-identifying code in the infinite hexagonal mesh with density (5r+2)/((r+2)(2r+1)) for even r and (5r+1)/((r+1)(2r+1)) for odd r. The optimal density of a (1,⩽2)-identifying code in the infinite hexagonal mesh is shown to be 2/3 and the optimal densities of (1,⩽3)- and (2,⩽3)-identifying codes are shown to be 1.

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Cited by (0)

1

Research supported by the Academy of Finland under grants 44002 and 200213.

2

Research supported by the Academy of Finland under grants 46186 and 207303.

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