# Subspace code constructions

## TL;DR

This paper advances the lower bounds on the size of certain subspace codes in projective geometry and introduces new non-equivalent orbit-codes, enhancing the understanding of subspace code constructions.

## Contribution

It improves the lower bounds for maximum subspace codes in PG(8,q) and constructs new non-equivalent orbit-codes for specific parameters.

## Key findings

- New lower bound for ${
m PG}(8,q)$ subspace codes.
- Construction of two new non-equivalent orbit-codes.
- Enhanced understanding of subspace code configurations.

## Abstract

We improve on the lower bound of the maximum number of planes of ${\rm PG}(8,q)$ mutually intersecting in at most one point leading to the following lower bound: ${\cal A}_q(9, 4; 3) \ge q^{12}+2q^8+2q^7+q^6+q^5+q^4+1$ for constant dimension subspace codes. We also construct two new non-equivalent $(6, (q^3-1)(q^2+q+1), 4; 3)_q$ constant dimension subspace orbit-codes.