On a generalization of the Deligne–Lusztig curve of Suzuki type and application to AG codes

Abstract

In this article, Algebraic-Geometric (AG) codes and quantum codes associated with a family of curves that includes the famous Suzuki curve are investigated. The Weierstrass semigroup at some rational point is computed. Notably, each curve in the family turns out to be a Castle curve over some finite field and a weak Castle curve over its extensions. This is a relevant feature when codes constructed from the curve are considered.

Keywords

• ag codes
• quantum codes
• deligne–lusztig curves
• 94b27