In coding theory, the Lee distance is a distance between two strings
Contents
Considering the alphabet as the additive group Zq, the Lee distance between two single letters
If
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.
History and application
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.
The Berlekamp code is an example of code in the Lee metric. Other significant examples are the Preparata code and Kerdock code; these codes are non-linear when considered over a field, but are linear over a ring.
Also, there exists a Gray isometry (bijection preserving weight) between