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Abstract Let q be a power of a prime and F q be a finite field with q elements. In this paper, we propose four families of infinite classes of permutation trinomials having the form c x − x s + x q s , and investigate the relationship between two types of widely discussed permutation polynomials. Based on this relation, many classes of permutation polynomials having the form (x q k − x + δ) s + c x without restriction on δ are derived. [ABSTRACT FROM AUTHOR]

This note presents two classes of permutation polynomials of the form $$(x^{p^m}-x+\delta )^s+L(x)$$ over the finite fields $${{\mathbb {F}}}_{p^{2m}}$$ as a supplement of the recent works of Zha, Hu and Li, Helleseth and Tang. [ABSTRACT FROM AUTHOR]

In this paper, two-to-one mappings and involutions without any fixed point on finite fields of even characteristic are investigated. First, we characterize a closed relationship between them by implicit functions and develop an AGW-like criterion for 2-to-1 mappings. Using this criterion, some new constructions of 2-to-1 mappings are proposed and eight classes of 2-to-1 mappings of the form (x 2 k + x + δ) s + c x are obtained. Finally, a number of classes of involutions without any fixed point are derived from the known 2-to-1 mappings by the relation between them. [ABSTRACT FROM AUTHOR]