Huang, Yan; Kai, Xiaoshan; Wan, Jinlong Construction of cyclic self-orthogonal codes over \(\mathbb{Z}_{p^2}\). (Chinese. English summary) Zbl 1389.94109 J. Syst. Sci. Math. Sci. 36, No. 12, 2473-2480 (2016). 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 Keywords:cyclic code; reciprocal polynomial; self-dual code; self-orthogonal code PDFBibTeX XMLCite \textit{Y. Huang} et al., J. Syst. Sci. Math. Sci. 36, No. 12, 2473--2480 (2016; Zbl 1389.94109)