Abstract
Self-dual cyclic codes over rings and their generalizations have become of interest due to their rich algebraic structures and wide applications. Cyclic and self-dual cyclic codes over the ring have been quite well studied, where p is a prime, k is a positive integer, and $$u^2=0$$ . We focus on negacyclic codes over , where p is an odd prime and k is a positive integer. An alternative and explicit algebraic characterization of negacyclic codes of length $$p^s$$ over is presented. Based on this result, representation and enumeration of self-dual negacyclic codes of length $$p^s$$ over are given under both the Euclidean and Hermitian inner products.
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