Orthogonal systems of polynomials in finite fields
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- by H. Niederreiter PDF
- Proc. Amer. Math. Soc. 28 (1971), 415-422 Request permission
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.References
- L. Carlitz, Invariantive theory of equations in a finite field, Trans. Amer. Math. Soc. 75 (1953), 405–427. MR 57912, DOI 10.1090/S0002-9947-1953-0057912-6 —, Invariant theory of systems of equations in a finite field, J. Analyse Math.
- Leonard Eugene Dickson, General theory of modular invariants, Trans. Amer. Math. Soc. 10 (1909), no. 2, 123–158. MR 1500831, DOI 10.1090/S0002-9947-1909-1500831-X
- V. A. Kurbatov and N. G. Starkov, The analytic representation of permutations, Sverdlovsk. Gos. Ped. Inst. Učen. Zap. 31 (1965), 151–158 (Russian). MR 0215817
- Harald Niederreiter, Permutation polynomials in several variables over finite fields, Proc. Japan Acad. 46 (1970), no. 10, suppl. to 46 (1970), no. 9, 1001–1005. MR 0288100
- Harald Niederreiter, Permutation polynomials in several variables, Acta Sci. Math. (Szeged) 33 (1972), 53–58. MR 309894
Additional Information
- © Copyright 1971 American Mathematical Society
- 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