Planarity of products of two linearized polynomials

被引:11
作者
Kyureghyan, Gohar [1 ]
Ozbudak, Ferruh [2 ,3 ]
机构
[1] Univ Magdeburg, Dept Math, D-39106 Magdeburg, Germany
[2] Middle E Tech Univ, Dept Math, TR-06800 Ankara, Turkey
[3] Middle E Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkey
关键词
Planar mapping; Quadratic mapping; Dembowski-Ostrom polynomial; Linearized polynomial; Directions defined by linear functions; Cubic irreducible polynomials; FINITE-FIELD; NUMBER; F-2(N);
D O I
10.1016/j.ffa.2012.08.008
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
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页码:1076 / 1088
页数:13
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