Planarity of products of two linearized polynomials

Date

2012-11-01

Author

KYUREGHYAN, Gohar
Özbudak, Ferruh

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Let L-1(x) and L-2(x) be linearized polynomials over F-qn. We give conditions when the product L-1(x) . L-2(x) defines a planar mapping on F-qn. For a polynomial L over F-qn, let M(L) = {alpha is an element of F-qn: L(x) + alpha . x is bijective on F-qn}. We show that the planarity of the product L-1(x) . L-2(x) is linked with the set M(L) of a suitable linearized polynomial L. We use this relation to describe families of such planar mappings as well as to obtain nonexistence results. (c) 2012 Elsevier Inc. All rights reserved.

Subject Keywords

Planar mapping, Quadratic mapping, Dembowski-Ostrom polynomial, Linearized polynomial, Directions defined by linear functions, Cubic irreducible polynomials

URI

https://hdl.handle.net/11511/49008

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2012.08.008

Collections

Department of Mathematics, Article

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Citation Formats

G. KYUREGHYAN and F. Özbudak, “Planarity of products of two linearized polynomials,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 1076–1088, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49008.