# Distance bounds for algebraic geometric codes

@article{Duursma2010DistanceBF, title={Distance bounds for algebraic geometric codes}, author={I. Duursma and R. Kirov and Seungkook Park}, journal={ArXiv}, year={2010}, volume={abs/1001.1374} }

Various methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor bound by Guneri-Stichtenoth-Taskin, and Duursma-Park, and of the order bound by Duursma-Park and Duursma-Kirov. In this paper we provide… Expand

#### 29 Citations

On the order bounds for one-point AG codes

- Computer Science, Mathematics
- Adv. Math. Commun.
- 2011

This work investigates in detail the application of the order bound for the minimum distance of algebraic geometry codes to one-point algebraIC geometry codes, obtaining a bound $d^*$ for theminimum distance of these codes and establishing a connection between that bound and its generalizations. Expand

On the Weight Hierarchy of Codes Coming From Semigroups With Two Generators

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2014

The formula obtained is applied to lower bounding the generalized Hamming weights, improving the bound given by Kirfel and Pellikaan in terms of the classical Feng-Rao distance and compared with a modification of the Griesmer bound. Expand

Two-Point Codes for the Generalized GK Curve

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2018

This work improves previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK), and finds several new improvements upon the MinT minimum distance tables. Expand

Delta sets for divisors supported in two points

- Computer Science, Mathematics
- Finite Fields Their Appl.
- 2012

General properties of delta sets are given and sequences of divisors supported in two points on Hermitian and Suzuki curves are analyzed. Expand

Lower bounds on the minimum distance in Hermitian one-point differential codes

- Mathematics
- 2013

Korchmáros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field… Expand

Fast Decoding of Dual Multipoint Codes From Algebraic Curves Up to the Kirfel–Pellikaan Bound

- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 2018

A fast method for decoding dual multipoint codes from algebraic curves up to the Kirfel–Pellikaan bound, based on the vectorial BMS algorithm with majority logic is presented, and it is shown that algebraic geometry codes from generic algebraic curve can be decodedup to the Goppa bound efficiently. Expand

Hermitian codes from higher degree places

- Mathematics
- 2013

Abstract Matthews and Michel (2005) [29] investigated the minimum distances of certain algebraic-geometry codes arising from a higher degree place P . In terms of the Weierstrass gap sequence at P ,… Expand

Feng-Rao decoding of primary codes

- Mathematics, Computer Science
- Finite Fields Their Appl.
- 2013

A very strong connection is demonstrated between Matsumoto and Miura’s bound and Andersen and Geilʼs bound when applied to primary one-point algebraic geometric codes, able to decode efficiently a large class of codes for which no non-trivial decoding algorithm was previously known. Expand

The minimum weights of two-point AG codes on norm-trace curves

- Mathematics, Computer Science
- Finite Fields Their Appl.
- 2018

It turns out that the order-like bound for two-point AG codes on norm-trace curves is better than that of one-point codes on the same curves except for a few cases. Expand

A G ] 2 0 Ju n 20 12 Hermitian codes from higher degree places

- 2018

Matthews and Michel [28] 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… Expand

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