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New Constant-Dimension Subspace Codes from Maximum Rank Distance Codes.
- Source :
- IEEE Transactions on Information Theory; Sep2018, Vol. 64 Issue 9, p6315-6319, 5p
- Publication Year :
- 2018
-
Abstract
- The main problem of constant-dimension subspace coding is to determine the maximal possible size ${\mathbf{A}}_{q}(n,d,k)$ of a set of $k$ -dimensional subspaces in ${\mathbf{F}}_{q}^{n}$ such that the subspace distance satisfies $d(U,V) \geq d$ for any two different subspaces $U$ and $V$ in this set. In this paper, we give a direct construction of constant-dimension subspace codes from two parallel versions of maximum rank-distance codes. The problem about the sizes of our constructed constant-dimension subspace codes is transformed into finding a suitable sufficient condition to restrict number of the roots of $L_{1}(L_{2}(x))-x$ where $L_{1}$ and $L_{2}$ are $q$ -polynomials over the extension field ${\mathbf{F}}_{q^{n}}$. New lower bounds for ${\mathbf{A}}_{q}(4k,2k,2k)$ , ${\mathbf{A}}_{q}(4k+2,2k,2k+1)$ , and ${\mathbf{A}}_{q}(4k+2,2(k-1),2k+1)$ are presented. Many new constant-dimension subspace codes better than previously best known codes with small parameters are constructed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 64
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 131346495
- Full Text :
- https://doi.org/10.1109/TIT.2018.2839596