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Lee Metric

The Lee metric on Z^n is the metric d_L(x,y)=sum_(i=1)^(n)|x_i-y_i|. For an integer q>=2, on (Z/qZ)^n it uses the shorter cyclic distance in each coordinate instead. An integer Lee ball of radius r is B_L(n,r)={x in Z^n:sum_(i)|x_i|<=r} (Golomb and Welch 1970).

The Golomb-Welch conjecture concerns tilings of Z^n by translates of these balls.

See also

Golomb-Welch Conjecture, Taxicab Metric

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References

Golomb, S. W. and Welch, L. R. "Perfect Codes in the Lee Metric and the Packing of Polyominoes." SIAM J. Appl. Math. 18, 302-317, 1970. https://doi.org/10.1137/0118025.

Cite this as:

Weisstein, Eric W. "Lee Metric." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LeeMetric.html

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