In this paper, necessary and sufficient conditions for the reversibility of a cyclic code of arbitrary length over a finite commutative chain ring have been derived. MDS reversible cyclic codes having length p^s over a finite chain ring with nilpotency index 2 have been characterized and a few examples of MDS reversible cyclic codes have been presented. Further, it is shown that the torsion codes of a reversible cyclic code over a finite chain ring are reversible. Also, an example of a non-reversible cyclic code for which all its torsion codes are reversible has been presented to show that the converse of this statement is not true. The cardinality and Hamming distance of a cyclic code over a finite commutative chain ring have also been determined.

翻译：本文推导了有限交换链环上任意长度循环码可逆性的充要条件。刻画了幂零指数为2的有限链环上长度为p^s的MDS可逆循环码，并给出了若干MDS可逆循环码的实例。进一步证明：有限链环上可逆循环码的挠码具有可逆性。同时，通过构造一个全体挠码均可逆但非可逆的循环码实例，说明该命题的逆命题不成立。此外，还确定了有限交换链环上循环码的基数与汉明距离。