Permutation decoding in group codes

The aim of this work is to study a permutation decoding algorithm for group codes. We focus exclusively on the case where [Formula: see text] is semisimple. In this setting, [Formula: see text] decomposes as the direct sum of a two-sided ideal associated with a group code and another two-sided ideal, and both of them are generated by central idempotent elements of [Formula: see text]. Furthermore, we define the notion of a GPD-set, which is essential for the construction of a generalized permutation decoding algorithm. This algorithm can be applied in certain cases where the classical permutation decoding algorithm is not applicable.