Permutation polynomials over finite fields involving x + xp + ... + xqa-1

Let p be a prime and q=p^s. For integer a>=0, let S"a=x+x^q+...+x^q^^^a^^^-^^^[email protected]?F"p[x]. We present three constructions of permutation polynomials of F"q"^"e involving S"a which generalize several recent results. When q is even, the third construction produces a large class of Dembowski-Ostrom permutation polynomials. We also discuss an interesting linear algebraic problem arising from the third construction.

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