Planarity of products of two linearized polynomials

KYUREGHYAN G., ÖZBUDAK F.

FINITE FIELDS AND THEIR APPLICATIONS, vol.18, no.6, pp.1076-1088, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 6
  • Publication Date: 2012
  • Doi Number: 10.1016/j.ffa.2012.08.008
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1076-1088
  • Keywords: Planar mapping, Quadratic mapping, Dembowski-Ostrom polynomial, Linearized polynomial, Directions defined by linear functions, Cubic irreducible polynomials, FINITE-FIELD, NUMBER, F-2(N)
  • Middle East Technical University Affiliated: Yes

Abstract

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.