In this work, a unique set of generators for a cyclic code over a finite chain ring has been established. The minimal spanning set and rank of the code have also been determined. Further, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code have been obtained. Some examples of optimal cyclic codes have also been presented.

翻译：本文建立了有限链环上循环码生成元的唯一集合，确定了该码的最小生成集及秩。进一步，得到了循环码成为MDS码及MHDR码的充分必要条件。文中还给出了一些最优循环码的示例。