Abstract
Permutation modulation codes are a class of group codes for the Gaussian channel whose codewords are obtained by permuting the components of a given initial vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> in Euclidean <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -dimensional space. In this paper, the problem of choosing the components of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> in such a way that the minimum distance between any two codewords is maximized is solved. In particular, a closed-form expression is obtained for this minimum distance and is used to investigate the asymptotic behavior of some selected codes.
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