Abstract
Permutation trinomials over finite fields are of great interest for their simple algebraic forms and important applications in many areas of mathematics and engineering. In this paper, six new classes of permutation trinomials over \(\mathbb {F}_{3^{3k}}\) are presented based on the multivariate method. Their permutation properties are proved by using the resultant elimination method.
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Acknowledgements
The authors would like to thank the anonymous referees for their valuable comments and helpful suggestions which improved both the quality and presentation of this paper. This work is supported by the National Natural Science Foundation of China (Grant 61672414 and 11571005), the National Cryptography Development Fund under Grant MMJJ20170113, and the 111 Project under Grant B08038.
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Wang, Y., Zha, Z. & Zhang, W. Six new classes of permutation trinomials over \(\mathbb {F}_{3^{3k}}\). AAECC 29, 479–499 (2018). https://doi.org/10.1007/s00200-018-0353-3
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DOI: https://doi.org/10.1007/s00200-018-0353-3