Hermitian codes from higher degree places

Abstract

Matthews and Michel investigated the minimum distances in certain algebraic-geometry codes arising from a higher degree place $P$. In terms of the Weierstrass gap sequence at $P$, they proved a bound that gives an improvement on the designed minimum distance. In this paper, we consider those of such codes which are constructed from the Hermitian function field. We determine the Weierstrass gap sequence $G(P)$ where $P$ is a degree 3 place, and compute the Matthews and Michel bound with the corresponding improvement. We show more improvements using a different approach based on geometry. We also compare our results with the true values of the minimum distances of Hermitian 1-point codes, as well as with estimates due Xing and Chen.

References in corpus (1)

• The dual minimum distance of arbitrary dimensional algebraic--geometric codes

Cited by in corpus (8)

• Weierstrass Semigroups from Kummer Extensions
• Multi-point Codes over Kummer Extensions
• Weierstrass Semigroup, Pure Gaps and Codes on Function Fields
• Weierstrass Pure Gaps From a Quotient of the Hermitian Curve
• On the minimum distance and the minimum weight of Goppa codes from a quotient of the Hermitian curve
• Multi-point Codes from Generalized Hermitian Curves
• Estimating The Dimension Of The Subfield Subcodes of Hermitian Codes
• Explicit Construction of AG Codes from Generalized Hermitian Curves