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On self-dual constacyclic codes of length ps over Fpm + uFpm

Authors: 

Hai Q. Dinh, Yun Fan, Hualu Liu, Xiusheng Liu, Songsak Sriboonchitta

Source title: 
Discrete Mathematics, 341(2): 324-335, 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

The aim of this paper is to establish all self-dual λ-constacyclic codes of length pover 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.