Construction of Subspace Codes through Linkage

TL;DR

This paper introduces a method to construct long subspace codes by linking shorter codes with rank metric codes, achieving optimal subspace distances and enabling efficient decoding, with applications to partial spreads.

Contribution

The paper presents a novel linkage construction for subspace codes that preserves minimum distance and includes a parallelizable decoding algorithm.

Findings

Constructed long subspace codes with optimal distance

Reproduced the best known partial spreads

Developed a parallel decoding algorithm

Abstract

A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as the minimum subspace distance of the constituent codes. As a special application, the construction of the best known partial spreads is reproduced. Finally, for a special case of linkage, a decoding algorithm is presented which amounts to decoding with respect to the smaller constituent codes and which can be parallelized.