Self dual and MHDR dual cyclic codes over finite chain rings

In this work, we establish a minimal set of generators for the dual code of a cyclic code having arbitrary length over a finite chain ring. It is observed that this set of generators forms a minimal strong Grobner basis for the dual code. Using this structure for the dual of a cyclic code, we obtain sufficient as well as necessary conditions for a cyclic code to be a self dual code over a finite chain ring. We enumerate the distinct non-trivial self dual cyclic codes over these rings. Further, we determine all MHDR dual cyclic codes. We provide a few examples of self dual and MHDR dual cyclic codes over various finite chain rings.