A class of constacyclic codes over \({\mathbb {Z}}_{4}[u]/\langle u^{k}\rangle \)

  • Habibul Islam
  • Tushar Bag
  • Om PrakashEmail author
Original Research


In this paper, we study \(\lambda \)-constacyclic and skew \(\lambda \)-constacyclic codes over the ring \({\mathbb {Z}}_{4}[u]/\langle u^{k}\rangle \) where \(u^{k}=0 \) with \(\lambda =(1+2u^{k-1})\) and \((3+2u^{k-1})\). It is shown that the Gray images of \(\lambda \)-constacyclic and skew \(\lambda \)-constacyclic codes over the ring \({\mathbb {Z}}_{4}[u]/\langle u^{k}\rangle \) are cyclic, quasi-cyclic, permutation equivalent to a QC code over \({\mathbb {Z}}_{4}\). Further, the generators of these \(\lambda \)-constacyclic codes over \({\mathbb {Z}}_{4}[u]/\langle u^{k}\rangle \) are obtained.


Constacyclic code Quasi-cyclic code Gray map Skew constacyclic code 

Mathematics Subject Classification

94B05 94B15 94B35 94B60 



The authors are thankful to the University Grants Commission (UGC), Govt. of India for financial support and Indian Institute of Technology Patna for providing the research facilities. The authors would like to thank the anonymous referees and the editor for their valuable suggestions to improve the presentation of the manuscript.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology PatnaPatnaIndia

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