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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 ⋯ 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 ⋯ p t . [ABSTRACT FROM AUTHOR]

In this paper, two new classes of entanglement-assisted quantum MDS codes (EAQMDS codes for short) with length n being a factor of q 2 ± 1 are presented via cyclic codes over finite fields of odd characteristic. Among our constructions, there are several EAQMDS codes with new parameters which have never been reported. Moreover, some of them have much larger minimum distance than known results. [ABSTRACT FROM AUTHOR]