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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The authors would like to thank the anonymous referees for very helpful comments.
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P. Choosuwan was partially supported by the Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT). S. Jitman was supported by the Thailand Research Fund and Silpakorn University under Research Grant RSA6280042.
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Choosuwan, P., Jitman, S. & Udomkavanich, P. A note on self-dual negacyclic codes of length \(p^s\) over 
.
European Journal of Mathematics 6, 1424–1437 (2020). https://doi.org/10.1007/s40879-019-00378-9
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DOI: https://doi.org/10.1007/s40879-019-00378-9