Permutation code: Difference between revisions

Revision as of 08:58, 9 April 2023

Revision as of 07:51, 22 April 2023

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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>