Cyclic self-orthogonal codes over finite chain ring.

In this paper, we study the cyclic self-orthogonal codes over a finite commutative chain ring ℤ p m , where p is a prime number. A generating polynomial of cyclic self-orthogonal codes over ℤ p m is obtained. We also provide a necessary and sufficient condition for the existence of nontrivial self-orthogonal codes over ℤ p m . Finally, we determine the number of the above codes with length n over ℤ p m for any (p , n) = 1. The results are given by Zhe-Xian Wan on cyclic codes over Galois rings in [Z. Wan, Cyclic codes over Galois rings, Algebra Colloq.6 (1999) 291–304] are extended and strengthened to cyclic self-orthogonal codes over ℤ p m . [ABSTRACT FROM AUTHOR]