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Paley type sets from cyclotomic classes and Arasu–Dillon–Player difference sets

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Abstract

In this paper, we present constructions of abelian Paley type sets by using multiplicative characters of finite fields and Arasu–Dillon–Player difference sets. The constructions produce many new Paley type sets and their configurations that were previous unknown in our classification of Paley type sets in finite fields of small orders.

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Acknowledgments

Y. Q. Chen would like to thank the Department of Mathematics at Zhejiang University for the hospitality he received during his visit when this research was initiated. The work of T. Feng was supported in part by the Fundamental Research Funds for the Central Universities, Zhejiang Provincial Natural Science Foundation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wright State University, Dayton, OH, 45435, USA

    Yu Qing Chen

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Tao Feng

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  1. Yu Qing Chen
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  2. Tao Feng
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Correspondence to Yu Qing Chen.

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Communicated by D. Jungnickel.

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Chen, Y.Q., Feng, T. Paley type sets from cyclotomic classes and Arasu–Dillon–Player difference sets. Des. Codes Cryptogr. 74, 581–600 (2015). https://doi.org/10.1007/s10623-013-9881-9

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  • DOI: https://doi.org/10.1007/s10623-013-9881-9

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