On permutation and complete permutation binomials and trinomials from linearized polynomials over finite fields
Manpreet Singhms44167@gmail.comDepartment of Mathematics and StatisticsHimachal Pradesh UniversityShimla, Himachal Pradesh, 171005, India0000-0002-3961-3571View full profile → , *Shalini GuptaCorresponding authorshalini.garga1970@gmail.comDepartment of Mathematics and StatisticsHimachal Pradesh UniversityShimla, Himachal Pradesh, 171005, India0000-0001-7743-0744View full profile → , P. L. Sharmaplsharma1964@gmail.comDepartment of Mathematics and StatisticsHimachal Pradesh UniversityShimla, Himachal Pradesh, 171005, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Dec 2022
- Published Online:
- 01 May 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1836
- Pages:
- 1073–1085
Abstract
Keywords
Subject Classifications
References
[1] Bassalygo, L. A. and Zinoviev, V. A., Permutation and complete permutation polynomials, Finite Fields and Their Applications, 33:2, 198-211 (2015).
[2] Baumbaugh, T. and Manganiello, F., Matroidal root structure of skew polynomials over finite fields, Journal of Discrete Mathematical Sciences and Cryptography, 22:3, 377-389 (2019), DOI: 10.1080/09720529.2019.1600845.
[3] Charpin, P. and Kyureghyan, G. M., On a class of permutation polynomials over International Conference on Sequences and their Applications, Springer, Berlin, Heidelberg, 368-376 (2008).
[4] Ding, C., Qu, L., Wang, Q., Yuan, J. and Yuan, P., Permutation trinomials over finite fields with even characteristic, SIAM Journal of Discrete Mathematics, 29:1, 79-92 (2015).
[5] Gupta, R. and Sharma, R. K., Some new classes of permutation trinomials over finite fields with even characteristic, Finite Fields and Their Applications, 41, 89-96 (2016).
[6] Guangkui, X. and Cao, X., Complete permutation polynomials over finite fields of odd characteristic, Finite Fields and Their Applications, 31, 228-240 (2015).
[7] Hou, X. D., A class of permutation binomials over finite fields, Journal of Number Theory, 133:10, 3549-3558 (2013).
[8] Hou, X. D., A class of permutation trinomials over finite fields (2013), arXiv:1303.0568.
[9] Hou, X. D. and Lappano, S. D., Determination of a type of permutation binomials over finite fields, Journal of Number Theory, 147, 14-23 (2015).
[10] Hou, X. D., Permutation polynomials over finite fields - a survey of recent advances, Finite Fields and Their Applications, 32, 82-119 (2015).
[11] Lidl R. and Niederreiter H., Finite Fields, Encyclopedia of Mathematics and its Applications, Addison-Wesley, Reading, MA, Vol. 20 (1983).
[12] Li, K., Qu, L. and Chen, X., New classes of permutation binomials and permutation trinomials over finite fields, Finite Fields and Their Applications, 43, 69-85 (2017).
[13] Ma, J., Zhang, T., Feng, T. and Ge, G., Some new results on permutation polynomials over finite fields, Design Codes and Cryptography, 83:2, 425-443 (2017).
[14] Mesnager, S., Kim, K. H. and Jo, H. S., On the number of rational zeros of linearized polynomials and the second order non linearity of cubic boolean functions, Cryptography and Communications, 12:4, 659-674 (2020).
[15] Mesnager, S., Kim, K. H., Choe, J. H. and Lee, D. N., Solving some affine equation over finite fields, Finite Fields and Their Applications, 68, 101746 (2020).
[16] Mesnager, S., Kim, K. H., Choe, J. H., Lee, D. N. and Go, D. S., Solving Cryptography and Communications, 12:4, 809-817 (2020).
[17] Mullen, G. L. and Panario D., Handbook of finite fields, Chapman and Hall, London (2013).
[18] Ore, O., On a special class of polynomials, Transactions of the American Mathematical Society, 34, 559-584 (1933).
[19] Tu, Z., Zeng, X. and Hu, L., Several classes of complete permutation polynomials, Finite Fields and Their Applications, 25, 182-193 (2014).
[20] Tu, Z. and Zeng, X., A class of permutation trinomials over finite fields of odd characteristic, Cryptography and Communications, 11, 563-58 (2019).
[21] Wu, D., Yuan, P., Ding, C. and Ma, Y., Permutation trinomials over Finite Fields and Their Applications, 46, 38-56 (2017).
[22] Wu, G., Li, N., Helleseth, T. and Zhang, Y., Some classes of monomial complete permutation polynomials over finite fields of characteristic two, Finite Fields and Their Applications, 28, 148-165 (2014).
[23] Yi, H. B., Nie, Z. and Li, B., Efficient implementations of Gaussian elimination in finite fields on ASICs for MQ cryptographic systems, Journal of Discrete Mathematical Sciences and Cryptography, 21:3, 797-802 (2018), DOI: 10.1080/09720529.2018.1449354.
[24] Zeng, X., Zhu, X. and Hu, L., Two new permutation polynomials with the form over Applicable Algebra in Engineering, Communication and Computing, 21:2, 145-150 (2010).
[25] Zieve, M., On some permutation polynomials over of the form Proceedings of the American Mathematical Society, 137:7, 2209-2216 (2009).
