On the Lattice of Cyclic Linear Codes Over Finite Chain Rings

Let R be a commutative finite chain ring of invariants (q ,s ). In this paper, the trace representation of any free cyclic R -linear code of length l, is presented, via the q -cyclotomic cosets modulo l, when gcd(l,q ) = 1. The lattice Cy(R,l);+,∩ of cyclic R -linear codes of length l, is investigated. A lower bound on the Hamming distance of cyclic R -linear codes of length l , is established. When q is even, a family of MDS and self-orthogonal R -linear cyclic codes, is constructed.