On Constacyclic Codes over $$\boldsymbol{Z}_{\boldsymbol{p}_{1}\boldsymbol{p}_{2}\cdots\boldsymbol{p}_{\boldsymbol{t}}}$$

Abstract

Let t ≥ 2 be an integer, and let p1, ⋯, pt be distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring $${Z_{{p_1}{p_2} \cdots {p_t}}}$$ and the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over $${Z_{{p_1}{p_2} \cdots {p_t}}}$$ .