Lee distance

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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 {0, 1, …, q − 1} of size q ≥ 2. It is a metric, defined as

\sum_{i=1}^n \min(|x_i-y_i|,q-|x_i-y_i|).

If q = 2 the Lee distance coincides with the Hamming distance.

The metric space induced by the Lee distance is a discrete analog of the elliptic space.


If q = 6, then the Lee distance between 3140 and 2543 is 1 + 2 + 0 + 3 = 6.

History and application[edit]

The Lee distance is named after C. Y. Lee. It is applied for phase modulation while the Hamming distance is used in case of orthogonal modulation.