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On pseudorandom sequences of \(k\) symbols constructed using finite fields

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Abstract

A family of pseudorandom sequences of \(k\) symbols are constructed by using finite fields of prime-power order. The construction is an extension of certain construction of Sárközy and Winterhof on binary sequences using the quadratic character with polynomial arguments over any finite fields, and of certain construction of Ahlswede, Mauduit and Sárközy on sequences of \(k\) symbols using multiplicative characters with polynomial arguments over finite prime fields. Certain pseudorandom measures of the resulting sequences are considered.

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Acknowledgments

The authors wish to thank the anonymous referees for their patience in reading this manuscript and their invaluable comments and suggestions. They also wish to thank Zhixiong Chen for discussing and comments. X.N.D. was partially supported by the National Natural Science Foundation of China under grants 61202395, 61103199 and 61163038, the Program for New Century Excellent Talents in University (NCET-12-0620) and the Natural Science Foundation of Gansu Province of China under Grant 1208RJZA255. Z.X.L. was partially supported by the National Natural Science Foundation of China under Grant No. 61373140 and the Special Scientific Research Program in Fujian Province Universities of China under Grant No. JK2013044.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou , 730070, Gansu, People’s Republic of China

    Xiaoni Du

  2. The State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an , 710071, Shaanxi, People’s Republic of China

    Xiaoni Du

  3. School of Mathematics, Putian University, Putian , 351100, Fujian, People’s Republic of China

    Zhixing Lin

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  1. Xiaoni Du
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Correspondence to Xiaoni Du.

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Du, X., Lin, Z. On pseudorandom sequences of \(k\) symbols constructed using finite fields. AAECC 25, 265–285 (2014). https://doi.org/10.1007/s00200-014-0224-5

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  • DOI: https://doi.org/10.1007/s00200-014-0224-5

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