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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Orthogonal systems of polynomials in finite fields


Author: H. Niederreiter
Journal: Proc. Amer. Math. Soc. 28 (1971), 415-422
MSC: Primary 12C05
DOI: https://doi.org/10.1090/S0002-9939-1971-0291136-9
MathSciNet review: 0291136
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Abstract: The notion of an orthogonal system of polynomials in several variables in finite fields is introduced which generalizes a concept of orthogonality by Kurbatov and Starkov. Necessary and sufficient conditions for orthogonality in terms of character sums and permutation polynomials are given. Results of Carlitz on systems of equations in finite fields and earlier results of the author on permutation polynomials in several variables are generalized.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0291136-9
Keywords: Orthogonal systems of polynomials, permutation polynomials, equations in finite fields
Article copyright: © Copyright 1971 American Mathematical Society