Index bounds for value sets of polynomials over finite fields (Q2811685)
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scientific article; zbMATH DE number 6592290
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Index bounds for value sets of polynomials over finite fields |
scientific article; zbMATH DE number 6592290 |
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10 June 2016
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polynomials
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value set
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index
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degree
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0.93382263
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0.93176544
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0.9286758
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0.9275569
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0.9210011
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0.91788405
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0.91580224
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0.91344714
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0.9072661
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Index bounds for value sets of polynomials over finite fields (English)
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The index \(\ell\) of a polynomial \(g(x)\) over the finite field of \(q\) elements was introduced by \textit{A. Akbary} et al. [Finite Fields Appl. 15, No. 2, 195--206 (2009; Zbl 1220.11145)]. The main result of the paper is the following:NEWLINENEWLINEIf \(g(x)\) is not a permutation polynomial, then the value set \(V_g\) of \(g(x)\) is of size at most NEWLINE\[NEWLINE|V_g|\leq q-\frac{q-1}{\ell}.\tag{*}NEWLINE\]NEWLINENEWLINENEWLINEMoreover, the authors generalize the concept of index to multivariate vector polynomials and generalize (*).NEWLINENEWLINEFor the entire collection see [Zbl 1314.11002].
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