Trace- and norm-compatible extensions of finite fields (Q1205131)
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scientific article; zbMATH DE number 146889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Trace- and norm-compatible extensions of finite fields |
scientific article; zbMATH DE number 146889 |
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Trace- and norm-compatible extensions of finite fields (English)
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1 April 1993
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The author defines the notion of trace-compatibility in analogy to the notion of norm-compatibility for extensions of a field. Extensions that are norm-compatible or trace-compatible are computationally easier to handle. An algorithm for the computation of trace-compatible polynomials is given. The number of distinct (norm- or trace-) compatible polynomials of fixed degree is counted. There are two misprints: p. 200 4th line from the bottom: \(F_{q^ m}\) must be \(F_{q^ m}^*\), p. 201 line 21: log must be Log. The paper is written in a very compact way and therefore it has become more or less opaque. The results, however, are nice.
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extension fields
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finite fields
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normal bases
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primitive elements
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trace- compatibility
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norm-compatibility
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algorithm
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computation of trace- compatible polynomials
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