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In coding theory, the Lee distance is a distance between two strings x 1 x 2 … x n {\displaystyle x_{1}x_{2}\dots x_{n}} and y 1 y 2 … y n {\displaystyle 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
Considering the alphabet as the additive group Zq, the Lee distance between two single letters x {\displaystyle x} and y {\displaystyle y} is the length of shortest path in the Cayley graph between them.
If q = 2 {\displaystyle q=2} or q = 3 {\displaystyle q=3} the Lee distance coincides with the Hamming distance, because both distances are 0 for two single equal symbols and 1 for two single non-equal symbols. For q > 3 {\displaystyle q>3} this is not the case anymore, the Lee distance can become bigger than 1.