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The asymptotic behavior of Grassmannian codes
- Publication Year :
- 2011
-
Abstract
- 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.<br />Comment: 5 pages
- Subjects :
- Computer Science - Discrete Mathematics
94B60
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1111.2713
- Document Type :
- Working Paper