For any odd prime \(p\not =5\), the structures of cyclic codes of length \(5p^s\) over \(\mathbb F_{p^m}\) are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes.

对于任何奇素数\(p\not =5\)，长度\(5p^s\)超过\(\mathbb F_{p^m}\)的循环码结构被用于构造量子纠错码（简称，QEC 代码）。提供了一些新的 QEC 代码，因为它们的参数与所有以前的结构不同。我们给出了所有由 CSS 构造构造的量子最大距离可分（简称 qMDS 代码）。我们还构建了量子同步代码（简称 QSC）。为了丰富可用 QSC 的种类，我们构建了许多新的 QSC 来说明我们的结果。其中，有比已知的原始窄义 BCH 码更短的长度和更大的最小距离的 QSCs 码。