Repeated-root constacyclic codes of prime power lengths over finite chain rings

• Main Authors: Hai Q. Dinh, Hien D.T. Nguyen, Songsak Sriboonchitta, Thang M. Vo
• Format: Journal
• Published: 2018
• Subjects: Engineering; Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84988737040&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/57380
• Institution: Chiang Mai University

© 2016 Elsevier Inc. We study the algebraic structure of repeated-root λ-constacyclic codes of prime power length psover a finite commutative chain ring R with maximal ideal 〈γ〉. It is shown that, for any unit λ of the chain ring R, there always exists an element r∈R such that λ−rpsis not invertible, and furthermore, the ambient ring R[x]〈xps−λ〉 is a local ring with maximal ideal 〈x−r,γ〉. When there is a unit λ0such that λ=λ0ps, the nilpotency index of x−λ0in the ambient ring R[x]〈xps−λ〉 is established. When λ=λ0ps+γw, for some unit w of R, it is shown that the ambient ring R[x]〈xps−λ〉 is a chain ring with maximal ideal 〈xps−λ0〉, which in turn provides structure and sizes of all λ-constacyclic codes and their duals. Among other things, situations when a linear code over R is both α- and β-constacyclic, for different units α, β, are discussed.