# Multi-point codes over Kummer extensions

@article{Hu2016MultipointCO, title={Multi-point codes over Kummer extensions}, author={Chuangqiang Hu and Shudi Yang}, journal={Designs, Codes and Cryptography}, year={2016}, volume={86}, pages={211-230} }

This paper is concerned with the construction of algebraic geometric codes defined from Kummer extensions. It plays a significant role in the study of such codes to describe bases for the Riemann–Roch spaces associated with totally ramified places. Along this line, we present an explicit characterization of Weierstrass semigroups and pure gaps. Additionally, we determine the floor of a certain type of divisor introduced by Maharaj, Matthews and Pirsic. Finally, we apply these results to find…

## 11 Citations

### Multi-point Codes from the GGS Curves

- Computer Science, MathematicsAdv. Math. Commun.
- 2020

The Weierstrass semigroups and pure gaps are characterized explicitly and the floor of a certain type of divisor is determined and the properties of AG codes from GGS curves are investigated.

### Weierstrass Semigroups From a Tower of Function Fields Attaining the Drinfeld-Vladut Bound

- MathematicsArXiv
- 2019

The third function field in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vl-du-t bound is investigated and the Weierstrass semigroups and pure gaps at several places on F^{(3)} are calculated.

### Weierstrass Pure Gaps From a Quotient of the Hermitian Curve

- MathematicsArXiv
- 2017

The numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves.

### Pure Weierstrass gaps from a quotient of the Hermitian curve

- MathematicsFinite Fields Their Appl.
- 2018

### Weierstrass semigroups on the third function field in a tower attaining the Drinfeld-Vlăduţ bound

- Computer ScienceAdvances in Mathematics of Communications
- 2022

The third function field is investigated in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vlăduţ bound and the Weierstrass semigroups and pure gaps at several places are calculated.

### Interactive oracle proofs of proximity to algebraic geometry codes

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2020

This work constructs an Interactive Oracle Proof of Proximity (IOPP) for some families of AG codes by generalizing an IOPP for Reed-Solomon codes, known as the FRI protocol [9].

### Pure gaps on curves with many rational places

- Computer Science, MathematicsFinite Fields Their Appl.
- 2018

### On Weierstrass Gaps at Several Points

- MathematicsBulletin of the Brazilian Mathematical Society, New Series
- 2018

We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado (Proc…

### On Weierstrass Gaps at Several Points

- MathematicsBulletin of the Brazilian Mathematical Society, New Series
- 2018

We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado (Proc…

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