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Erschienen in: Applicable Algebra in Engineering, Communication and Computing 5/2015

01.11.2015 | Original Paper

Some permutation polynomials over finite fields

verfasst von: José E. Marcos

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 5/2015

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Abstract

This paper shows new permutation polynomials over finite fields. Some of them are of the form \(\left( x^{p^k}\pm x+\delta \right) ^s +hx\). Some others are complete mappings.

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Literatur
1.
Zurück zum Zitat Akbary, A., Ghioca, D., Wang, Q.: On constructing permutation polynomials of finite fields. Finite Fields Appl. 17, 51–67 (2011)MATHMathSciNetCrossRef Akbary, A., Ghioca, D., Wang, Q.: On constructing permutation polynomials of finite fields. Finite Fields Appl. 17, 51–67 (2011)MATHMathSciNetCrossRef
2.
Zurück zum Zitat Ball, S., Zieve, M.: Symplectic spreads and permutation polynomials. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds.) Finite Fields and Applications, Lecture Notes in Computer Science, vol. 2948, pp. 79–88. Springer, Berlin (2004) Ball, S., Zieve, M.: Symplectic spreads and permutation polynomials. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds.) Finite Fields and Applications, Lecture Notes in Computer Science, vol. 2948, pp. 79–88. Springer, Berlin (2004)
3.
Zurück zum Zitat Blokhuis, A., Coulter, R.S., Henderson, M., O’Keefe, C.M.: Permutations amongst the Dembowski–Ostrom polynomials. In: Jungnickel, D., Niederreiter, H. (eds.) Finite Fields and Applications: Proceedings of the Fifth International Conference on Finite Fields and Applications, pp. 37–42. Springer, Berlin (2001)CrossRef Blokhuis, A., Coulter, R.S., Henderson, M., O’Keefe, C.M.: Permutations amongst the Dembowski–Ostrom polynomials. In: Jungnickel, D., Niederreiter, H. (eds.) Finite Fields and Applications: Proceedings of the Fifth International Conference on Finite Fields and Applications, pp. 37–42. Springer, Berlin (2001)CrossRef
4.
Zurück zum Zitat Budaghyan, L., Carlet, C., Leander, G.: Two classes of quadratic APN binomials inequivalent to power functions. IEEE Trans. Inf. Theory 54, 4218–4229 (2008)MATHMathSciNetCrossRef Budaghyan, L., Carlet, C., Leander, G.: Two classes of quadratic APN binomials inequivalent to power functions. IEEE Trans. Inf. Theory 54, 4218–4229 (2008)MATHMathSciNetCrossRef
5.
Zurück zum Zitat Cao, X., Hu, L.: New methods for generating permutation polynomials over finite fields. Finite Fields Appl. 17, 493–503 (2011)MATHMathSciNetCrossRef Cao, X., Hu, L.: New methods for generating permutation polynomials over finite fields. Finite Fields Appl. 17, 493–503 (2011)MATHMathSciNetCrossRef
6.
Zurück zum Zitat Cohen, S.D.: Exceptional polynomials and the reducibility of substitution polynomials. Enseign. Math. 36(2), 53–65 (1990)MATHMathSciNet Cohen, S.D.: Exceptional polynomials and the reducibility of substitution polynomials. Enseign. Math. 36(2), 53–65 (1990)MATHMathSciNet
7.
8.
Zurück zum Zitat Ding, C., Xiang, Q., Yuan, J., Yuan, P.: Explicit classes of permutation polynomials of \({\mathbb{F}}_{3^{3m}}\). Sci. China Ser. A 53, 639–647 (2009)MathSciNetCrossRef Ding, C., Xiang, Q., Yuan, J., Yuan, P.: Explicit classes of permutation polynomials of \({\mathbb{F}}_{3^{3m}}\). Sci. China Ser. A 53, 639–647 (2009)MathSciNetCrossRef
9.
Zurück zum Zitat Dobbertin, H.: Almost perfect nonlinear power functions on GF\((2^n)\): the Welch case. IEEE Trans. Inf. Theory 45, 1271–1275 (1999)MATHMathSciNetCrossRef Dobbertin, H.: Almost perfect nonlinear power functions on GF\((2^n)\): the Welch case. IEEE Trans. Inf. Theory 45, 1271–1275 (1999)MATHMathSciNetCrossRef
10.
Zurück zum Zitat Helleseth, T., Zinoviev, V.: New Kloosterman sums identities over \(F_{2^m}\) for all \(m\). Finite Fields Appl. 9, 187–193 (2003)MATHMathSciNetCrossRef Helleseth, T., Zinoviev, V.: New Kloosterman sums identities over \(F_{2^m}\) for all \(m\). Finite Fields Appl. 9, 187–193 (2003)MATHMathSciNetCrossRef
13.
14.
Zurück zum Zitat Li, N., Helleseth, T., Tang, X.: Further results on a class of permutation polynomials over finite fields. Finite Fields Appl. 22, 16–23 (2013)MATHMathSciNetCrossRef Li, N., Helleseth, T., Tang, X.: Further results on a class of permutation polynomials over finite fields. Finite Fields Appl. 22, 16–23 (2013)MATHMathSciNetCrossRef
15.
16.
Zurück zum Zitat Mullen, G.L., Niederreiter, H.: Dickson polynomials over finite fields and complete mappings. Can. Math. Bull. 30, 19–27 (1987)MATHMathSciNetCrossRef Mullen, G.L., Niederreiter, H.: Dickson polynomials over finite fields and complete mappings. Can. Math. Bull. 30, 19–27 (1987)MATHMathSciNetCrossRef
17.
18.
Zurück zum Zitat Tu, Z., Zeng, X., Jiang, Y.: Two classes of permutation polynomials having the form \((x^{2^m}+x+\delta )^s+x\). Finite Fields Appl. 31, 12–24 (2015)MATHMathSciNetCrossRef Tu, Z., Zeng, X., Jiang, Y.: Two classes of permutation polynomials having the form \((x^{2^m}+x+\delta )^s+x\). Finite Fields Appl. 31, 12–24 (2015)MATHMathSciNetCrossRef
19.
Zurück zum Zitat Tu, Z., Zeng, X., Li, C., Helleseth, T.: Permutation polynomials of the form \((x^{p^m}-x+\delta )^s+L(x)\) over the finite field \({\mathbb{F}}_{p^{2m}}\) of odd characteristic. Finite Fields Appl. 34, 20–35 (2015)MathSciNetCrossRef Tu, Z., Zeng, X., Li, C., Helleseth, T.: Permutation polynomials of the form \((x^{p^m}-x+\delta )^s+L(x)\) over the finite field \({\mathbb{F}}_{p^{2m}}\) of odd characteristic. Finite Fields Appl. 34, 20–35 (2015)MathSciNetCrossRef
20.
Zurück zum Zitat Wu, B., Lin, D.: On constructing complete permutation polynomials over finite fields of even characteristic. Discrete Appl. Math. 184, 213–222 (2015)MathSciNetCrossRef Wu, B., Lin, D.: On constructing complete permutation polynomials over finite fields of even characteristic. Discrete Appl. Math. 184, 213–222 (2015)MathSciNetCrossRef
21.
Zurück zum Zitat Yuan, J., Ding, C.: Four classes of permutation polynomials of \({\mathbb{F}}_{2^m}\). Finite Fields Appl. 13, 869–876 (2007)MATHMathSciNetCrossRef Yuan, J., Ding, C.: Four classes of permutation polynomials of \({\mathbb{F}}_{2^m}\). Finite Fields Appl. 13, 869–876 (2007)MATHMathSciNetCrossRef
22.
Zurück zum Zitat Yuan, J., Ding, C.: Permutation polynomials over finite fields from a powerful lemma. Finite Fields Appl. 17, 560–574 (2011)MATHMathSciNetCrossRef Yuan, J., Ding, C.: Permutation polynomials over finite fields from a powerful lemma. Finite Fields Appl. 17, 560–574 (2011)MATHMathSciNetCrossRef
23.
24.
Zurück zum Zitat Yuan, J., Ding, C., Wang, H., Pieprzyk, J.: Permutation polynomials of the form \((x^p-x+\delta )^s + L(x)\). Finite Fields Appl. 14, 482–493 (2008)MATHMathSciNetCrossRef Yuan, J., Ding, C., Wang, H., Pieprzyk, J.: Permutation polynomials of the form \((x^p-x+\delta )^s + L(x)\). Finite Fields Appl. 14, 482–493 (2008)MATHMathSciNetCrossRef
25.
26.
Zurück zum Zitat Zeng, X., Zhu, X., Hu, L.: Two new permutation polynomials with the form \((x^{2^k}+x+\delta )^s+x\) over \({\mathbb{F}}_{2^n}\). Appl. Algebra Eng. Commun. Comput. 21, 145–150 (2010)MATHMathSciNetCrossRef Zeng, X., Zhu, X., Hu, L.: Two new permutation polynomials with the form \((x^{2^k}+x+\delta )^s+x\) over \({\mathbb{F}}_{2^n}\). Appl. Algebra Eng. Commun. Comput. 21, 145–150 (2010)MATHMathSciNetCrossRef
27.
Zurück zum Zitat Zieve, M.E.: Exceptional polynomials. In: Mullen, G.L., Panario, D. (eds.) Handbook of Finite Fields, pp. 236–240. CRC Press, Boca Raton (2013) Zieve, M.E.: Exceptional polynomials. In: Mullen, G.L., Panario, D. (eds.) Handbook of Finite Fields, pp. 236–240. CRC Press, Boca Raton (2013)
Metadaten
Titel
Some permutation polynomials over finite fields
verfasst von
José E. Marcos
Publikationsdatum
01.11.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Applicable Algebra in Engineering, Communication and Computing / Ausgabe 5/2015
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-015-0260-9