Fractional dimensional semifield planes (Q2856412)
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scientific article; zbMATH DE number 6220490
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fractional dimensional semifield planes |
scientific article; zbMATH DE number 6220490 |
Statements
28 October 2013
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semifield
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binary Knuth semifield
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fractional dimension
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subplane
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0.8908589
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0.86586356
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0.86345637
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0.8592009
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Fractional dimensional semifield planes (English)
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The dimension of an affine plane \(\pi\) of order \(n\) relative to a subplane \(\pi_0\) of order \(m\) is defined as \(\log_m n\). If \(\pi\) is Desarguesian, then this dimension is an integer. The authors provide several examples of semifields of order \(2^t, t\) odd, having a subfield of order 4. The corresponding translation planes thus have dimension \(t\over 2\) over a translation subplane.
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