Repeated-root constacyclic codes of prime power length over [Formula presented] and their duals

© 2016 Elsevier B.V. The units of the chain ring [formula presented] are partitioned into a distinct types. It is shown that for any unit Λ of Type k, a unit λ of Type k∗can be constructed, such that the class of λ-constacyclic of length psof Type k∗codes is one-to-one correspondent to the class of...

Full description

Saved in:
Bibliographic Details
Main Authors: Hai Q. Dinh, Sompong Dhompongsa, Songsak Sriboonchitta
Format: Journal
Published: 2018
Subjects:
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84977522194&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55948
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Chiang Mai University
Description
Summary:© 2016 Elsevier B.V. The units of the chain ring [formula presented] are partitioned into a distinct types. It is shown that for any unit Λ of Type k, a unit λ of Type k∗can be constructed, such that the class of λ-constacyclic of length psof Type k∗codes is one-to-one correspondent to the class of Λ-constacyclic codes of the same length of Type k via a ring isomorphism. The units of Raof the form Λ=Λ0+uΛ1+⋯+ua−1Λa−1, where Λ0,Λ1,…,Λa−1∈Fpm, Λ0≠0,Λ1≠0, are considered in detail. The structure, duals, Hamming and homogeneous distances of Λ-constacyclic codes of length psover Raare established. It is shown that self-dual Λ-constacyclic codes of length psover Raexist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α- and β-constacyclic over Rafor different units α, β.