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== Definition and properties ==
A permutation code <math>C</math> is defined as a subset of the [[Symmetric group|Symmetric Group]] in <math>S_n</math> endowed with the usual [[Hamming distance]] between strings of length <math>n</math>. More precisely, if <math>\sigma, \tau</math> are permutations in <math>S_n</math>, then <math>d(\tau, \sigma) = |\left \{ i \in \{1, 2, ..., n\} : \sigma(i) \neq \tau(i) \right \}|</math>
The minimum distance of a permutation code <math>C</math> is defined to be the minimum positive integer <math>d_{min}</math> such that there exist <math>\sigma, \tau</math> <math>\in</math> <math>C</math>, distinct, such that <math>d(\sigma, \tau) = d_{min} </math>.
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