期刊论文

Zheng, LJ

英文

Finite Fields and Their Applications

1071-5797

2023

91

102250

10.1016/j.ffa.2023.102250

The authors are grateful to the Editor and the anonymous reviewers for their valuable comments which have highly improved the manuscript. Especially, the reviewers pointed out that the permutation pentanomial presented in Theorem 3.3 can be generated by Algorithm 2.4 in [14] or Theorem 5.1 in [50] , and we have emphasized it in Remark 3.4 . This research is partly supported by Hunan Provincial Natural Science Foundation of China (Grant No. 2023JJ30517 ), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 19B485 ), China Scholarship Council, and Open Research Program of Shanghai Key Lab of Intelligent Information Processing (Grant No. IIPL201902 ).

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In this paper, we further push the studies on permutation polynomials over the finite fields Fq2 with q=2m. We find the coefficients of f(x)=x+a1xs1(q−1)+1+a2xs2(q−1)+1+a3xs3(q−1)+1+a4xs4(q−1)+1+a5xs5(q−1)+1 over Fq2 that lead f(x) to be a permutation for [Formula presented] in case of a5=0, and find more new (si) such that f(x) is a permutation hexanomial of Fq2 with coefficients in F4. Some well-known results are covered by our results. The numerical results suggest that the sufficient conditions we find in the first class of p...