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On the Planarity of Certain Dembowski-Ostrom Polynomials

Journal: Süleyman Demirel University Faculty of Arts and Science Journal of Science (Vol.17, No. 2)

Publication Date:

Authors : ; ;

Page : 261-269

Keywords : Planar mappings; Linearized polynomials; Dembowski-Ostrom polynomials;

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Planar mappings, defined by Dembowski and Ostrom, are identified as a means to construct projective planes. Then, many important applications of planar mappings appear in different fields such as cryptography and coding theory. In this paper, we provide sufficient and necessary conditions for the planarity of certain Dembowski-Ostrom polynomials over the finite field extension of degree three with odd characteristic. In particular, we completely determine the coefficients of the given Dembowski-Ostrom polynomials to be planar.

Last modified: 2022-12-08 18:02:46