The fraction of subspaces of \(\text{GF}(q)^ n\) with a specified number of minimal weight vectors is asymptotically Poisson (Q1378491)
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scientific article; zbMATH DE number 1117988
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The fraction of subspaces of \(\text{GF}(q)^ n\) with a specified number of minimal weight vectors is asymptotically Poisson |
scientific article; zbMATH DE number 1117988 |
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The fraction of subspaces of \(\text{GF}(q)^ n\) with a specified number of minimal weight vectors is asymptotically Poisson (English)
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12 February 1998
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Summary: The weight of a vector in the finite vector space \(\text{GF}(q)^n\) is the number of nonzero components it contains. We show that for a certain range of parameters \((n,j,k,w)\) the number of \(k\)-dimensional subspaces having \(j(q-1)\) vectors of minimum weight \(w\) has asymptotically a Poisson distribution with parameter \(\lambda={n\choose w}(q-1)^{w-1}q^{k-n}\). As the Poisson parameter grows, the distribution becomes normal.
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vector
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weight
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Poisson distribution
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