On the Planarity of Certain Dembowski-Ostrom Polynomials
Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, vol.17, no.2, pp.261-269, 2022 (TRDizin)
- Publication Type: Article / Article
- Volume: 17 Issue: 2
- Publication Date: 2022
- Doi Number: 10.29233/sdufeffd.1053097
- Journal Name: Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi
- Journal Indexes: Academic Search Premier, CAB Abstracts, Veterinary Science Database, zbMATH, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
- Page Numbers: pp.261-269
- Open Archive Collection: AVESIS Open Access Collection
- Süleyman Demirel University Affiliated: Yes
Abstract
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.