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In coding theory , the Lee distance is a distance between two strings and of equal length n over the q-ary alphabet -LCB- 0 , 1 , ... , q − 1 -RCB- of size q ≥ 2 .. coding theory. coding theory. distance. distance. alphabet. alphabet. It is a metric , defined as. metric. Metric ( mathematics ). Considering the alphabet as the additive group Zq , the Lee distance between two single letters and is the length of shortest path in the Cayley graph -LRB- which is circular since the group is cyclic -RRB- between them .. distance. distance. alphabet. alphabet. Cayley graph. Cayley graph. If or 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 .. distance. distance. Hamming distance. Hamming distance. For this is not the case anymore , the Lee distance can become bigger than 1 .. distance. distance. The metric space induced by the Lee distance is a discrete analog of the elliptic space .. distance. distance. metric. Metric ( mathematics ). metric space. metric space. elliptic space. Elliptic geometry