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Cryptography and Communications

, Volume 9, Issue 2, pp 241–272 | Cite as

A mass formula for negacyclic codes of length 2 k and some good negacyclic codes over \(\mathbb {Z}_{4}+u\mathbb {Z}_{4}\)

  • Rama Krishna BandiEmail author
  • Maheshanand Bhaintwal
  • Nuh Aydin
Article

Abstract

In this paper, we study negacyclic codes of length 2 k over the ring \(R=\mathbb {Z}_{4}+u\mathbb {Z}_{4}\), u 2 = 0. We have obtained a mass formula for the number of negacyclic of length 2 k over R. We have also determined the number of self-dual negacyclic codes of length 2 k over R. This study has been further generalized to negacyclic codes of any even length using discrete Fourier transform approach over R. We have conducted an exhaustive search and obtained some new \(\mathbb {Z}_{4}\)-linear codes with good parameters.

Keywords

Codes over \(\mathbb {Z}_{4}+u\mathbb {Z}_{4}\) Negacyclic codes Cyclic codes Repeated root cyclic codes 

Mathematics Subject Classification (2010)

94B05 94B60 

Notes

Acknowledgments

The authors would like to thank anonymous referees for their careful reading and valuable suggestions which greatly improved the final presentation of the manuscript. The first author greatly acknowledges the financial support given by Ministry of Human Resources and Development, India.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Rama Krishna Bandi
    • 1
    Email author
  • Maheshanand Bhaintwal
    • 1
  • Nuh Aydin
    • 2
  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Mathematics and StatisticsKenyon CollegeGambierUSA

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