A new class of permutation polynomials of \(\mathbb F_q\) (Q372489)
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scientific article; zbMATH DE number 6213863
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new class of permutation polynomials of \(\mathbb F_q\) |
scientific article; zbMATH DE number 6213863 |
Statements
A new class of permutation polynomials of \(\mathbb F_q\) (English)
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8 October 2013
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permutation polynomials
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polynomials over finite fields
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0.9438541
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0.9359931
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0.9356358
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0.93327487
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0.9321314
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0.9310254
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0.9308618
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Using only elementary arguments, the authors prove that NEWLINE\[NEWLINE f(x)=x^u\big(x^{\frac{q-1}{2}}+x^{\frac{q-1}{4}}+1\big)\in\mathbb{F}_q[x] NEWLINE\]NEWLINE (for a prime power \(q=p^r\) and a positive integer \(u\)) is a permutation polynomial if \(u\) and \(q-1\) are relatively prime, \(q\equiv 1\bmod 8\), and \(3^{\frac{q-1}{4}}\equiv 1\bmod p\).
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