On the number of polynomials over \(\mathrm{GF}(2)\) that factor into \(2, 3\) or \(4\) prime polynomials (Q1071058)
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scientific article; zbMATH DE number 3937283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of polynomials over \(\mathrm{GF}(2)\) that factor into \(2, 3\) or \(4\) prime polynomials |
scientific article; zbMATH DE number 3937283 |
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On the number of polynomials over \(\mathrm{GF}(2)\) that factor into \(2, 3\) or \(4\) prime polynomials (English)
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1985
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Let \(N_ e(d)\) denote the number of polynomials of degree \(d\) over \(\mathrm{GF}(2)\) that factorize into \(e\) prime polynomials. Formulae for \(N_ e(d)\), in terms of the Möbius function, are obtained for \(e=2,3\), and \(4\); the values are tabulated for some values of \(d\leq 127\), and compared with the asymptotic formulae.
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polynomials over GF(2)
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factorization of polynomials
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asymptotic formulae
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