Veronese subspace codes

TL;DR

This paper constructs a new family of constant dimension subspace codes in projective space using a correspondence between quadrics and points, achieving specific parameters for error correction.

Contribution

It introduces a novel construction of subspace codes based on the relationship between quadrics in PG(2,q) and points in PG(5,q).

Findings

Constructed a family of subspace codes with specified parameters.

Achieved codes with parameters: (6, q^3(q^2-1)(q-1)/3 + (q^2+1)(q^2+q+1), 4; 3)_q.

Demonstrated the use of geometric correspondences in code construction.

Abstract

Using the correspondence between quadrics of ${\rm PG}(2,q)$ and points of ${\rm PG}(5,q)$, a family of $(6,q^3(q^2-1)(q-1)/3+(q^2+1)(q^2+q+1),4;3)_q$ constant dimension subspace codes is constructed.