Two types of permutation polynomials with special forms
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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 cx-x^s + x^qs over F_q^2, and investigate the relationship between this type of permutation polynomials with that of the form (x^q-x+δ)^s+cx. Based on this relation, many classes of permutation trinomials having the form (x^q-x+δ)^s+cx without restriction on δ over F_q^2 are derived from known permutation trinomials having the form cx-x^s + x^qs.
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