An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary field (Q802667)
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scientific article; zbMATH DE number 4198136
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary field |
scientific article; zbMATH DE number 4198136 |
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An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary field (English)
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1990
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By evaluating some Kloosterman sums the author obtains a formula for the number of irreducible polynomials of degree n over GF(2) such that the coefficients of x and \(x^{n-1}\) are 1. From this formula it readily can be seen that this number is always positive. Therefore such polynomials exist for arbitrarily large degrees. They can be used in the construction of irreducible self-reciprocal polynomials over GF(2).
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Kloosterman sums
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irreducible polynomials
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