On the lattice of cyclic codes over finite chain rings

Abstract

In this paper, R is a finite chain ring of invariants (q, s), and l is a positive integer fulfilling gcd(l, q) = 1. In the language of q-cyclotomic cosets modulo l, the cyclic codes over R of length l are uniquely decomposed into a direct sum of trace- representable cyclic codes over R and the lattice of cyclic codes over R of length l is investigated.