Any network codes comes from an algebraic curve taking osculating spaces

TL;DR

This paper demonstrates that any network code over a finite field can be represented using osculating spaces of a smooth projective algebraic curve, linking network coding to algebraic geometry.

Contribution

It establishes a novel geometric realization of network codes via osculating spaces of algebraic curves, bridging coding theory and algebraic geometry.

Findings

Any network code over _q can be realized through osculating spaces of a smooth projective curve.

Provides a geometric construction method for network codes.

Connects network coding with algebraic geometry concepts.

Abstract

In this note we prove that every network code over $\mathbb {F}_q$ may be realized taking some of the osculating spaces of a smooth projective curve.