Quadratic permutations, complete mappings and mutually orthogonal latin squares

We investigate the permutation behavior of a special class of Dembowski-Ostrom polynomials over a finite field of characteristic 2 of the form ) = )( )+ )) where , , are linearized polynomials. To our knowledge, the given class has not been studied previously in the literature. We identify several n...

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Bibliographic Details
Published inMathematica Slovaca Vol. 67; no. 5; pp. 1129 - 1146
Main Authors Samardjiska, Simona, Gligoroski, Danilo
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 26.10.2017
Walter de Gruyter GmbH
Subjects
20N05
Arrays
complete mappings
DO polynomials
Equivalence
Functions (mathematics)
Latin square design
Mathematical analysis
MOLS
permutation polynomials
Permutations
Polynomials
Primary 12Y05
quasigroup polynomials
Secondary 14G50
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Summary:We investigate the permutation behavior of a special class of Dembowski-Ostrom polynomials over a finite field of characteristic 2 of the form ) = )( )+ )) where , , are linearized polynomials. To our knowledge, the given class has not been studied previously in the literature. We identify several new types of permutation polynomials of this class. While most of the newly identified polynomials are linearly equivalent to permutation monomials, we show that there exist subclasses that are not affine equivalent to monomials, and we describe their forms. One of the newly identified classes contains a subclass of complete mappings. We use these complete mappings to define new sets of mutually orthogonal Latin squares, as well as new vectorial bent functions from the Maiorana-McFarland class. Moreover, the quasigroup polynomials obtained in the process are different and inequivalent to the previously known ones.
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2017-0037