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On complementary dual multinegacirculant codes

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Abstract

Linear codes with complementary duals intersect with their duals trivially. Multinegacirculant codes that are complementary dual are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, whereas special choices of the co-index and base field size are needed for higher indices. Asymptotic existence results are derived for the special class of such codes that have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of complementary dual multinegacirculant codes with relative distance satisfying a modified Gilbert-Varshamov bound.

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Acknowledgments

We would like to thank the anonymous reviewers for their comments which improved the final version of the paper. Patrick Solé thanks Prof. Wolfmann for helpful discussions. Güneri is supported by TÜBİTAK project 215E200, which is associated with the SECODE project in the scope of CHIST-ERA Program. Solé is also supported by the SECODE project. This paper is a part of the Ph.D. dissertation of the fourth author. The third author was at Sabancı University when the article was submitted. Currently, she is with Nanyang Technological University.

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Authors and Affiliations

  1. Math Department, King Abdulaziz University, Jeddah, Saudi Arabia

    Adel Alahmadi & Hatoon Shoaib

  2. Sabancı University, FENS, 34956, Istanbul, Turkey

    Cem Güneri

  3. School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore

    Buket Özkaya

  4. CNRS, Centrale Marseille, I2M, Aix-Marseille Université, Marseille, France

    Patrick Solé

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  1. Adel Alahmadi
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  2. Cem Güneri
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  3. Buket Özkaya
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  4. Hatoon Shoaib
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  5. Patrick Solé
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Correspondence to Adel Alahmadi.

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Alahmadi, A., Güneri, C., Özkaya, B. et al. On complementary dual multinegacirculant codes. Cryptogr. Commun. 12, 101–113 (2020). https://doi.org/10.1007/s12095-019-00364-8

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  • DOI: https://doi.org/10.1007/s12095-019-00364-8

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