An upper bound for the p-rank of a translation plane (Q757832)
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scientific article; zbMATH DE number 4194573
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An upper bound for the p-rank of a translation plane |
scientific article; zbMATH DE number 4194573 |
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An upper bound for the p-rank of a translation plane (English)
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1991
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Let \(\Pi\) be a projective translation plane of order \(q=p^ m\), let M be the incidence matrix of \(\Pi\) and \(rk_ p(\Pi)\) the rank of M over GF(p). The authors prove the following inequality: \[ rk_ p(M)\leq q^ 2+q+1-\sum^{m-1}_{i=0}(-1)^ i\left( \begin{matrix} 2m\\ i\end{matrix} \right)\left( \begin{matrix} m+(m-i)p\\ 2m\end{matrix} \right). \]
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translation planes
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