Left dihedral codes over finite chain rings

Let R be a finite commutative chain ring, D 2 n the dihedral group of size and [ ] ring. In this paper, we completely characterize left ideals (called -codes) when gcd ( c h r ) , = 1 . way, explore structure some skew-cyclic codes length over also × S where is an isomorphic copy As particular result, give cyclic case F p m Galois field, classification for N -codes any positive integer both cases determine dual identify self-dual ones.