New classes of permutation quadrinomials over 𝔽<sub><i>q</i><sup>3</sup></sub>

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  • CHEN Changhui
    Mathematics and Science College of Shanghai Normal University
  • KAN Haibin
    Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University Shanghai Engineering Research Center of Blockchain Yiwu Research Institute of Fudan University
  • PENG Jie
    Mathematics and Science College of Shanghai Normal University
  • WANG Li
    Mathematics and Science College of Shanghai Normal University

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<p>Permutation polynomials have been studied for a long time and have important applications in cryptography, coding theory and combinatorial designs. In this paper, by means of the multivariate method and the resultant, we propose four new classes of permutation quadrinomials over 𝔽q3, where q is a prime power. We also show that they are not quasi-multiplicative equivalent to known ones. Moreover, we compare their differential uniformity with that of some known classes of permutation trinomials for some small q.</p>

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