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

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Abstract

In this paper, we study negacyclic codes of length 2k 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 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.

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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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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Rama Krishna Bandi & Maheshanand Bhaintwal

  2. Department of Mathematics and Statistics, Kenyon College, Gambier, OH, 43022, USA

    Nuh Aydin

Authors
  1. Rama Krishna Bandi
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  2. Maheshanand Bhaintwal
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  3. Nuh Aydin
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Correspondence to Rama Krishna Bandi.

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Bandi, R.K., Bhaintwal, M. & Aydin, N. A mass formula for negacyclic codes of length 2k and some good negacyclic codes over \(\mathbb {Z}_{4}+u\mathbb {Z}_{4}\) . Cryptogr. Commun. 9, 241–272 (2017). https://doi.org/10.1007/s12095-015-0172-3

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