Permutation code: Difference between revisions

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== Definition and Properties ==

A permutation code <math>C</math> can be defined as a subset of [[PermutationSymmetric 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 the permutation in <math>S_n</math>, then d(<math>\sigma, \tau</math>) <math>...</math>,

d(\tau, \sigma) = |\left \{ i \in \{1, 2, ..., n\} : \sigma(i) \neq \tau(i) \right \}|</math>

The minimum distance of a permutation code is defined to be the minimum positive integer <math>dd_{min}</math> such that there exist <math>\sigma, \tau</math> <math>\in</math> <math>S_nC</math> such that d(<math>d(\sigma, \tau</math>) = <math>dd_{min} </math>.

One of the reasons why permutation codes are suitable for certain channels is that alphabet symbols only appear once in each codeword, which for example makes the errors occurring in the context of [[Power-line communication|powerline]] communication less impactful on codewords

== Bounds ==