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When Is the Number of True Different Permutation Polynomials Equal to 0?

Author

Listed:
  • Lucian Trifina

    (Department of Telecommunications and Information Technologies, “Gheorghe Asachi” Technical University, Iasi 700506, Romania)

  • Daniela Tarniceriu

    (Department of Telecommunications and Information Technologies, “Gheorghe Asachi” Technical University, Iasi 700506, Romania)

Abstract

In this paper, we have obtained the prime factorization form of positive integers N for which the number of true different fourth- and fifth-degree permutation polynomials (PPs) modulo N is equal to zero. We have also obtained the prime factorization form of N so that the number of any degree PPs nonreducible at lower degree PPs, fulfilling Zhao and Fan (ZF) sufficient conditions, is equal to zero. Some conclusions are drawn comparing all fourth- and fifth-degree permutation polynomials with those fulfilling ZF sufficient conditions.

Suggested Citation

  • Lucian Trifina & Daniela Tarniceriu, 2019. "When Is the Number of True Different Permutation Polynomials Equal to 0?," Mathematics, MDPI, vol. 7(11), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1018-:d:280502
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    References listed on IDEAS

    as
    1. Lucian Trifina & Daniela Tarniceriu, 2019. "Correction to: The number of different true permutation polynomial based interleavers under Zhao and Fan sufficient conditions," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 70(1), pages 141-158, January.
    2. Lucian Trifina & Daniela Tarniceriu, 2016. "The number of different true permutation polynomial based interleavers under Zhao and Fan sufficient conditions," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(4), pages 593-623, December.
    3. Lucian Trifina & Daniela Tarniceriu, 2017. "A simple method to determine the number of true different quadratic and cubic permutation polynomial based interleavers for turbo codes," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(1), pages 147-171, January.
    4. Lucian Trifina & Daniela Tarniceriu, 2018. "Determining the number of true different permutation polynomials of degrees up to five by Weng and Dong algorithm," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 67(2), pages 211-215, February.
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    1. Lucian Trifina & Daniela Tarniceriu, 2019. "Correction to: The number of different true permutation polynomial based interleavers under Zhao and Fan sufficient conditions," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 70(1), pages 141-158, January.
    2. Lucian Trifina & Daniela Tarniceriu, 2018. "Determining the number of true different permutation polynomials of degrees up to five by Weng and Dong algorithm," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 67(2), pages 211-215, February.

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