Two-Point Codes for the Generalised GK curve

Élise Barelli; Peter  Beelen; Mrinmoy Datta; Vincent Neiger; Johan Sebastian Heesemann Rosenkilde

doi:10.1109/TIT.2017.2763165

Two-Point Codes for the Generalised GK curve

Élise Barelli, Peter Beelen, Mrinmoy Datta, Vincent Neiger, Johan Sebastian Heesemann Rosenkilde

École polytechnique

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Abstract

We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti–Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.

Original language	English
Journal	I E E E Transactions on Information Theory
Volume	64
Issue number	9
Pages (from-to)	6268-6276
Number of pages	9
ISSN	0018-9448
DOIs	https://doi.org/10.1109/TIT.2017.2763165
Publication status	Published - 2018

Keywords

AG code
GGK curve
Order bound
Two-point Weierstrass semigroup

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COFUNDPostdocDTU: COFUNDPostdocDTU
Præstrud, M. R. (Project Participant) & Brodersen, S. W. (Project Participant)
01/01/2014 → 31/12/2019
Project: Research

Cite this

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title = "Two-Point Codes for the Generalised GK curve",

abstract = "We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti–Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.",

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T1 - Two-Point Codes for the Generalised GK curve

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AU - Beelen, Peter

AU - Datta, Mrinmoy

AU - Neiger, Vincent

AU - Rosenkilde, Johan Sebastian Heesemann

PY - 2018

Y1 - 2018

N2 - We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti–Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.

AB - We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti–Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.

KW - AG code

KW - GGK curve

KW - Order bound

KW - Two-point Weierstrass semigroup

U2 - 10.1109/TIT.2017.2763165

DO - 10.1109/TIT.2017.2763165

M3 - Journal article

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VL - 64

SP - 6268

EP - 6276

JO - I E E E Transactions on Information Theory

JF - I E E E Transactions on Information Theory

IS - 9

ER -

Two-Point Codes for the Generalised GK curve

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Keywords

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