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

Derong Xie , Qunying Liao

Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 555 -566.

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Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 555 -566. DOI: 10.1007/s11401-019-0151-7
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On Constacyclic Codes over $\boldsymbol{Z}_{\boldsymbol{p}_{1}\boldsymbol{p}_{2}\cdots\boldsymbol{p}_{\boldsymbol{t}}}$

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Abstract

Let t ≥ 2 be an integer, and let p 1, ⋯, p t 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 ${Z_{{p_1}{p_2} \cdots {p_t}}}$.

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Ideal / Isomorphism / Constacyclic code / Self-orthogonal code / Self-orthogonal cyclic code

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Derong Xie,Qunying Liao. On Constacyclic Codes over $\boldsymbol{Z}_{\boldsymbol{p}_{1}\boldsymbol{p}_{2}\cdots\boldsymbol{p}_{\boldsymbol{t}}}$. Chinese Annals of Mathematics, Series B, 2019, 40(4): 555-566 DOI:10.1007/s11401-019-0151-7

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