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：在这项工作中，已经建立了一个有限链环上循环码的唯一生成元组。已确定了代码的最小生成集和秩。进一步，已经获得了一个循环码是MDS码的充分必要条件，以及循环码是MHDR码的充分必要条件。还介绍了一些最优循环码的例子。