Geodesic
The fraction of subspaces of \(\text{GF}(q)^ n\) with a specified number of minimal weight vectors is asymptotically Poisson
The electronic journal of combinatorics, Tome 4 (1997) no. 1
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The weight of a vector in the finite vector space $\mathrm{GF}(q)^n$ 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.
DOI : 10.37236/1288
Classification : 05A16, 05A15, 11T99
Mots-clés : vector, weight, Poisson distribution 
@article{10_37236_1288,
     author = {Edward A. Bender and E. Rodney Canfield},
     title = {The fraction of subspaces of {\(\text{GF}(q)^} n\) with a specified number of minimal weight vectors is asymptotically {Poisson}},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {1},
     doi = {10.37236/1288},
     zbl = {0885.05014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1288/}
}
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Edward A. Bender; E. Rodney Canfield. The fraction of subspaces of \(\text{GF}(q)^ n\) with a specified number of minimal weight vectors is asymptotically Poisson. The electronic journal of combinatorics, Tome 4 (1997) no. 1. doi: 10.37236/1288

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