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Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 693–700 | Cite as

Study on negacyclic codes over the ring \(\mathbb {Z}_{p}[u]/<u^{k+1}-u\)

  • Tushar BagEmail author
  • Ashish K. Upadhyay
Original Research
  • 120 Downloads

Abstract

In this paper, we study the properties of negacyclic codes over the ring \(R=\mathbb {Z}_{p}+u\mathbb {Z}_{p}+\dots +u^k\mathbb {Z}_{p} \), for odd prime p, using decomposition method. We have determined the generators of negacyclic and dual negacyclic codes. We have also established the necessary and sufficient condition for it to contains it’s dual. It is also shown that the \(\mathbb {Z}_p\)-Gray image of a negacyclic code of length n is a quasi negacyclic code of length 3n.

Keywords

Negacyclic code Quasi negacyclic code Gray map Dual code 

Mathematics Subject Classification

94B05 94B15 94B60 

Notes

Acknowledgements

The first author is thankful to University Grant Commission (UGC), Government of India for financial support under Sr. No. 2061441025 with Ref No. 22/06/2014(i)EU-V.

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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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