Further results on planar DO functions and commutative semifields |
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| Authors: | Guobiao Weng Xiangyong Zeng |
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| Institution: | 1.School of Mathematical Sciences,Dalian University of Technology,Liaoning,People’s Republic of China;2.Faculty of Mathematics and Computer Science,Hubei University,Hubei,People’s Republic of China |
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| Abstract: | It is proven that any Dembowski–Ostrom polynomial is planar if and only if its evaluation map is 2-to-1, which can be used
to explain some known planar Dembowski–Ostrom polynomials. A direct connection between a planar Dembowski–Ostrom polynomial
and a permutation polynomial is established if the corresponding semifield is of odd dimension over its nucleus. In addition,
all commutative semifields of order 35 are classified. |
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