# On the order sequence of an embedding of the Ree curve

## TL;DR

This paper computes the Weierstrass order-sequence for a linear series on the Ree curve, revealing that all Weierstrass points are rational over the base field, enhancing understanding of the curve's geometric properties.

## Contribution

It provides the explicit Weierstrass order-sequence for a linear series on the Ree curve and characterizes its Weierstrass points as all being rational over the base field.

## Key findings

- All Weierstrass points are $ extbf{F}_q$-rational.
- The order-sequence is explicitly computed.
- The set of Weierstrass points coincides with $ extbf{F}_q$-rational points.

## Abstract

In this paper we compute the Weierstrass order-sequence associated with a certain linear series on the Deligne-Lusztig curve of Ree type. As a result, we determine that the set of Weierstrass points of this linear series consists entirely of $\mathbb F_q$-rational points.