Combining subspace codes

Abstract

In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_q(n,d;k)$ of codes whose codewords are $k$-subspaces of ${\mathbb{F}}_q^n$ with minimum subspace distance $d$. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant--dimension subspace codes for many parameters, including $A_q(10,4;5)$, $A_q(12,4;4)$, $A_q(12,6,6)$ and $A_q(16,4;4)$.

17 pages; construction for A_(10,4;5) was flawed

References in corpus (1)

• A note on the linkage construction for constant dimension codes

Cited by in corpus (6)

• A note on the linkage construction for constant dimension codes
• Parameter-controlled inserting constructions of constant dimension subspace codes
• The interplay of different metrics for the construction of constant dimension codes
• New Constructions of Subspace Codes Using Subsets of MRD codes in Several Blocks
• Improving the Linkage Construction with Echelon-Ferrers for Constant-Dimension Codes
• New Construction for Constant Dimension Subspace Codes via a Composite Structure