Orthomorphism Polynomials of degree 7 over finite fields
Abstract
In 2019, Xiang Fan xfan classified all permutation polynomials of degree 7 over finite fields of odd characteristics. In this paper, we use this classification to determine the complete list of degree 7 orthomorphism polynomials over finite fields of order q∈\11,~13,~17,~19,~25,~49\. In addition, the non-existence of these polynomials is established for certain fields.
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