Coset Construction for Subspace Codes

Abstract

One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\mathrm{PG}(n,q)$, i.e., the set of subspaces of ${\mathbb{F}}_q^n$, for a given minimal distance. Here we generalize a construction of Etzion and Silberstein to a wide range of parameters. This construction, named coset construction, improves or attains several of the previously best-known subspace code sizes and attains the MRD bound for an infinite family of parameters.

18 pages, 2 tables

References in corpus (3)

• Construction of Large Constant Dimension Codes With a Prescribed Minimum Distance
• Tables of subspace codes
• Improved upper bounds for partial spreads

Cited by in corpus (12)

• Tables of subspace codes
• Combining subspace codes
• A note on the linkage construction for constant dimension codes
• Lifted codes and the multilevel construction for constant dimension codes
• Classification of large partial plane spreads in $PG(6,2)$ and related combinatorial objects
• Parameter-controlled inserting constructions of constant dimension subspace codes
• The interplay of different metrics for the construction of constant dimension codes
• New LMRD bounds for constant dimension codes and improved constructions
• Construction of Const Dimension Code from Two Parallel Versions of Linkage Construction
• New Construction for Constant Dimension Subspace Codes via a Composite Structure
• Improving the Linkage Construction with Echelon-Ferrers for Constant-Dimension Codes
• Multilevel inserting constructions for constant dimension subspace codes