Permutation decoding of group codes

We consider suboptimum decoding of group codes, represented in the form of a set of n-vectors whose components are obtained by permuting the components of an initial vector according to a certain group G of permutations. Permutation decoding consists of the following two steps. First, we decode the received vector by searching for the most likely permutation in the symmetric group S_n, next we select the element in G closest to the permutation found. Here we focus on the first step. In particular, we show how any group code can be represented as a permutation code, and we determine the minimum value of n