Abstract
In this paper, the theory of finite Coxeter groups is applied to group codes. The class of group codes generated by finite Coxeter groups is a generalization of the well-known permutation modulation codes of Slepian. As a main result, a simple set of linear equations is given to characterize the optimal solution to a restricted initial point problem for all these codes. In particular, it is found that Ingemarsson’s solution to the initial point problem for permutation modulation without sign changes is not always optimal. Moreover, a list of new good group codes in dimension 8 is presented. Finally, a new maximum-likelihood decoding algorithm is presented that has a reasonably low complexity and that applies to all codes generated by finite Coxeter groups.
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