Cryptography and Communications

, Volume 9, Issue 2, pp 241–272

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

  • Rama Krishna Bandi
  • Maheshanand Bhaintwal
  • Nuh Aydin

DOI: 10.1007/s12095-015-0172-3

Cite this article as:
Bandi, R.K., Bhaintwal, M. & Aydin, N. Cryptogr. Commun. (2017) 9: 241. doi:10.1007/s12095-015-0172-3


In this paper, we study negacyclic codes of length 2k over the ring \(R=\mathbb {Z}_{4}+u\mathbb {Z}_{4}\), u2 = 0. We have obtained a mass formula for the number of negacyclic of length 2k over R. We have also determined the number of self-dual negacyclic codes of length 2k 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.


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

Mathematics Subject Classification (2010)

94B05 94B60 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Rama Krishna Bandi
    • 1
  • 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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