New Construction for Constant Dimension Subspace Codes via a Composite Structure

TL;DR

This paper introduces a new construction method for constant dimension subspace codes using a composite structure of MRD codes, resulting in at least 49 new codes surpassing existing ones.

Contribution

It presents a novel construction approach combining MRD codes and sub-codes, significantly improving the known bounds for constant dimension subspace codes.

Findings

Constructed at least 49 new codes exceeding previous bests.

Demonstrated the advantage of the new construction over existing methods.

Validated the approach through extensive examples.

Abstract

One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) = \dim(U+V)-\dim(U\cap V) \geq d$ for any two different $k$-dimensional subspaces $U$ and $V$ in this set. In this paper, we propose a construction for constant dimension subspace codes by inserting a composite structure composing of an MRD code and its sub-codes. Its vast advantage over the previous constructions has been confirmed through extensive examples. At least $49$ new constant dimension subspace codes which exceeds the currently best codes are constructed.