Two-point AG codes from the Beelen-Montanucci maximal curve

Leonardo Landi; Lara Vicino

doi:10.1016/j.ffa.2022.102009

Two-point AG codes from the Beelen-Montanucci maximal curve

Leonardo Landi, Lara Vicino

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Abstract

In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-GüneriStichtenoth (GGS) curve are discovered.

Original language	English
Article number	102009
Journal	Finite Fields and Their Applications
Volume	80
Number of pages	17
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2022.102009
Publication status	Published - 2022

Keywords

AG codes
Beelen-Montanucci curve
Order bound
Two-point code
Two-point Weierstrass semigroup

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10.1016/j.ffa.2022.102009

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title = "Two-point AG codes from the Beelen-Montanucci maximal curve",

abstract = "In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-G{\"u}neriStichtenoth (GGS) curve are discovered.",

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AU - Landi, Leonardo

AU - Vicino, Lara

PY - 2022

Y1 - 2022

N2 - In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-GüneriStichtenoth (GGS) curve are discovered.

AB - In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a lower bound on the minimum distance of such codes. AG codes with better parameters with respect to comparable two-point codes from the Garcia-GüneriStichtenoth (GGS) curve are discovered.

KW - AG codes

KW - Beelen-Montanucci curve

KW - Order bound

KW - Two-point code

KW - Two-point Weierstrass semigroup

U2 - 10.1016/j.ffa.2022.102009

DO - 10.1016/j.ffa.2022.102009

M3 - Journal article

VL - 80

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

M1 - 102009

ER -

Two-point AG codes from the Beelen-Montanucci maximal curve

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Keywords

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