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Linear complexity of a class of pseudorandom sequences over a general finite field

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Abstract

Due to their nice algebraic structures and pseudorandom features, generalized cyclotomic sequences have wide applications in simulation, coding and cryptography. Based on the Ding–Helleseth sequence, Bai et al. proposed a class of balanced generalized sequences of length pq. Moreover, they showed that this class of sequences has high linear complexity over a finite field of order two. In this paper, we study the linear complexity and the minimal polynomial of this class of sequences over a general finite field. Results indicate the sequence considered possesses high linear complexity over a general finite field.

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Acknowledgements

This study was funded by Natural Science Foundation of China (Grant Number 61772292, 61772476), Natural Science Foundation of Fujian Province (Grant Number 2015J01237), Fujian Normal University Innovative Research Team (Grant Number IRTL1207).

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Authors and Affiliations

  1. School of Economics, Fujian Normal University, Fuzhou, 350117, Fujian, People’s Republic of China

    Qi Ye

  2. Fujian Provincial Key Laboratory of Network Security and Cryptology, College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350117, Fujian, People’s Republic of China

    Pinhui Ke

  3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Jian Shen

Authors
  1. Qi Ye
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  2. Pinhui Ke
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  3. Jian Shen
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Corresponding author

Correspondence to Pinhui Ke.

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All the authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.\(\mathbb {Z}\)

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Communicated by A. Di Nola.

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Ye, Q., Ke, P. & Shen, J. Linear complexity of a class of pseudorandom sequences over a general finite field. Soft Comput 22, 4335–4346 (2018). https://doi.org/10.1007/s00500-017-2870-6

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  • DOI: https://doi.org/10.1007/s00500-017-2870-6

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