On self-dual constacyclic codes of length p<sup>s</sup>over F<inf>p<sup>m</sup></inf>+uF<inf>p<sup>m</sup></inf>
© 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...
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| Main Authors: | , , , , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85029741424&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58822 |
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| Institution: | Chiang Mai University |
| Summary: | © 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. |
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