Combining subspace codes

TL;DR

This paper explores methods to combine subspace codes to improve lower bounds on their maximum size for various parameters in constant-dimension coding, advancing coding theory.

Contribution

It introduces new approaches for combining subspace codes, leading to improved lower bounds for several key parameters in constant-dimension codes.

Findings

Improved lower bounds for A_q(10, 4; 5)

Enhanced bounds for A_q(12, 4; 4)

Better bounds for A_q(12, 6, 6) and A_q(16, 4; 4)

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 $A_q(16, 4; 4)$.