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Construction of cyclic self-orthogonal codes over \(\mathbb{Z}_{p^2}\). (Chinese. English summary) Zbl 1389.94109

Summary: In this paper, the structure of cyclic self-orthogonal codes over the ring \(\mathbb{Z}_{p^2}\) of length \(n\) is studied, where \(n\) and \(p\) are relatively coprime and \(p\) is a prime. By using the generator polynomial of cyclic codes over \(\mathbb{Z}_{p^2}\) of length \(n\), a sufficient and necessary condition for the existence of cyclic self-orthogonal codes over \(\mathbb{Z}_{p^2}\) of length \(n\) is obtained. Further, a method of constructing cyclic self-orthogonal codes over \(\mathbb{Z}_{p^2}\) of length \(n\) is given and the number of such codes is determined.

MSC:

94B15 Cyclic codes
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