Abstract
Polynomials of type xq+2+bx over the field Fq2 and of type xq2+q+2+bx over Fq3, where q=pm>2 is a power of a prime p are considered. All cases when these polynomials are permutation polynomials are classified. Therefore, all cases when the polynomials b−1xq+2 over Fq2 and b−1xq2+q+2 over Fq3 are the complete permutation polynomials are enumerated.
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