# zbMATH — the first resource for mathematics

Some classes of permutation polynomials of the form $$(x^{p^m}-x+\delta)^s+x$$ over $$\mathbb{F}_{p^{2m}}$$. (English) Zbl 1336.05005
Summary: In this paper, some new classes of permutation polynomials with the form $$(x^{p^m}-x+\delta)^s + x$$ are investigated by determining the number of solutions of some equations over $$\mathbb{F}_{p^{2m}}$$.

##### MSC:
 11T06 Polynomials over finite fields
##### Keywords:
finite field; permutation polynomial; trace function
Full Text:
##### References:
 [1] Akbary, A.; Ghioca, D.; Wang, Q., On constructing permutations of finite fields, Finite Fields Appl., 17, 1, 51-67, (2011) · Zbl 1281.11102 [2] Berlekamp, E. R.; Rumsey, H.; Solomon, G., On the solution of algebraic equations over finite fields, Inf. Control, 10, 6, 553-564, (1967) · Zbl 0166.04803 [3] Helleseth, T.; Zinoviev, V., New Kloosterman sums identities over $$\mathbb{F}_{2^m}$$ for all m, Finite Fields Appl., 9, 2, 187-193, (2003) · Zbl 1081.11077 [4] Hou, X., Permutation polynomials over finite fields — a survey of recent advances, Finite Fields Appl., 32, 82-119, (2015) · Zbl 1325.11128 [5] Li, N.; Helleseth, T.; Tang, X., Further results on a class of permutation polynomials over finite fields, Finite Fields Appl., 22, 16-23, (2013) · Zbl 1285.05004 [6] Lidl, R.; Niederreiter, H., Finite fields, Encyclopedia of Mathematics and Its Applications, vol. 20, (1997), Cambridge University Press [7] Lachaud, G.; Wolfmann, J., The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Trans. Inf. Theory, 36, 3, 686-692, (1990) · Zbl 0703.94011 [8] Mullen, G. L.; Panario, D., Handbook of finite fields, (2013), Taylor & Francis Boca Raton · Zbl 1319.11001 [9] 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) · Zbl 1320.11120 [10] Tu, Z.; Zeng, X.; Li, C.; Helleseth, T., Permutation polynomials of the form $$(x^{p^m} - x + \delta)^s + L(x)$$, Finite Fields Appl., 34, 20-35, (2015) · Zbl 1315.05008 [11] Yuan, J.; Ding, C., Four classes of permutation polynomials of $$\mathbb{F}_{2^m}$$, Finite Fields Appl., 13, 4, 869-876, (2007) · Zbl 1167.11045 [12] Yuan, J.; Ding, C.; Wang, H.; Pieprzyk, J., Permutation polynomials of the form $$(x^p - x + \delta)^s + L(x)$$, Finite Fields Appl., 14, 2, 482-493, (2008) · Zbl 1211.11136 [13] Yuan, P.; Ding, C., Permutation polynomials over finite fields from a powerful lemma, Finite Fields Appl., 17, 6, 560-574, (2011) · Zbl 1258.11100 [14] Yuan, P.; Ding, C., Further results on permutation polynomials over finite fields, Finite Fields Appl., 27, 88-103, (2014) · Zbl 1297.11148 [15] Yuan, P.; Zheng, Y., Permutation polynomials from piecewise functions, Finite Fields Appl., 35, 215-230, (2015) · Zbl 1331.11108 [16] Zeng, X.; Tian, S.; Tu, Z., Permutation polynomials from trace functions over finite fields, Finite Fields Appl., 35, 36-51, (2015) · Zbl 1327.05009 [17] 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, 2, 145-150, (2010) · Zbl 1215.11116 [18] Zha, Z.; Hu, L., Two classes of permutation polynomials over finite fields, Finite Fields Appl., 18, 4, 781-790, (2012) · Zbl 1288.11111
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.