Planarity of products of two linearized polynomials

KYUREGHYAN G., ÖZBUDAK F.

FINITE FIELDS AND THEIR APPLICATIONS, cilt.18, sa.6, ss.1076-1088, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 6
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.ffa.2012.08.008
  • Dergi Adı: FINITE FIELDS AND THEIR APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1076-1088
  • Anahtar Kelimeler: Planar mapping, Quadratic mapping, Dembowski-Ostrom polynomial, Linearized polynomial, Directions defined by linear functions, Cubic irreducible polynomials, FINITE-FIELD, NUMBER, F-2(N)
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.