On self-dual constacyclic codes of length p^sover F<inf>p^m</inf>+uF<inf>p^m</inf>

• Main Authors: Hai Q. Dinh, Yun Fan, Hualu Liu, Xiusheng Liu, Songsak Sriboonchitta
• Format: Journal
• Published: 2018
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85029741424&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/58822
• Institution: Chiang Mai University

© 2017 Elsevier B.V. The aim of this paper is to establish all self-dual λ-constacyclic codes of length psover the finite commutative chain ring R=Fpm+uFpm, where p is a prime and u2=0. If λ=α+uβ for nonzero elements α,β of Fpm, the ideal 〈u〉 is the unique self-dual (α+uβ)-constacyclic codes. If λ=γ for some nonzero element γ of Fpm, we consider two cases of γ. When γ=γ−1, i.e., γ=1 or −1, we first obtain the dual of every cyclic code, a formula for the number of those cyclic codes and identify all self-dual cyclic codes. Then we use the ring isomorphism φ to carry over the results about cyclic accordingly to negacyclic codes. When γ≠γ−1, it is shown that 〈u〉 is the unique self-dual γ-constacyclic code. Among other results, the number of each type of self-dual constacyclic code is obtained.