The asymptotic behavior of Grassmannian codes

Details The asymptotic behavior of Grassmannian codes The asymptotic behavior of Grassmannian codes

2011-11-11

arxiv.org/abs/1111.2713v1

Computer Science

Discrete Mathematics

5 pages

Scientific paper

The iterated Johnson bound is the best known upper bound on a size of an error-correcting code in the Grassmannian $\mathcal{G}_q(n,k)$. The iterated Sch\"{o}nheim bound is the best known lower bound on the size of a covering code in $\mathcal{G}_q(n,k)$. We use probabilistic methods to prove that both bounds are asymptotically attained for fixed $k$ and fixed radius, as $n$ approaches infinity. We also determine the asymptotics of the size of the best Grassmannian codes and covering codes when $n-k$ and the radius are fixed, as $n$ approaches infinity.

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