Construction of Const Dimension Code from Two Parallel Versions of Linkage Construction

TL;DR

This paper introduces two parallel versions of the linkage construction to enhance constant dimension codes, achieving larger code sizes for given parameters and surpassing recent improvements in specific cases.

Contribution

It presents a novel parallel linkage construction method that improves code size for constant dimension codes over existing techniques.

Findings

Achieves larger code sizes for specific parameters

Surpasses recent linkage construction improvements

Applicable to codes with parameters (13,4,4), (17,4,4), (19,6,6)

Abstract

The linkage construction and its generalization is one of the most powerful constructions for constant dimension code, accounting for approximately 50\% of all the listed parameters. We show how to improve the linkage construction of subspace codes by two parallel versions of the linkage construction. This proof allows us to attain codes of larger size for a given minimum distance, which exceeds the latest improvements on the linkage construction \cite{combining2019Antonio} in the cases $A_q(13,4,4),A_q(17,4,4), A_q(19,6,6)$.