Permutation codes over finite chain rings are intro-duced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for exis-tence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a 2′-group, and the group action is transi-tive, the sufficient and necessary condition of the existence of permutation codes is given.
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