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Lee distance
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Lee distance : ウィキペディア英語版
Lee distance
In coding theory, the Lee distance is a distance between two strings x_1 x_2 \dots x_n and y_1 y_2 \dots y_n of equal length ''n'' over the ''q''-ary alphabet of size ''q'' ≥ 2.
It is a metric, defined as
: \sum_^n \min(|x_i-y_i|,q-|x_i-y_i|).
Considering the alphabet as the additive group Z''q'', the Lee distance between two letters is the length of shortest path in the Cayley graph (which is circular since the group is cyclic) between them.
If ''q'' = 2 or ''q'' = 3 the Lee distance coincides with the Hamming distance.
The metric space induced by the Lee distance is a discrete analog of the elliptic space.
==Example==
If ''q'' = 6, then the Lee distance between 3140 and 2543 is 1 + 2 + 0 + 3 = 6.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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