Intersections between the norm-trace curve and some low degree curves

Matteo Bonini; Massimiliano Sala

doi:10.1016/j.ffa.2020.101715

Intersections between the norm-trace curve and some low degree curves

Matteo Bonini^*
, Massimiliano Sala

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

5 Citations (Scopus)

45 Downloads (Pure)

Abstract

In this paper we analyze the intersection between the norm-trace curve over F_q³ and the curves of the form y=ax³+bx²+cx+d, giving a complete characterization of the intersection between the curve and the parabolas (a=0), as well as sharp bounds for the other cases. This information is used for the determination of the weight distribution of some one-point AG codes arising from the curve.

Original language	English
Article number	101715
Journal	Finite Fields and Their Applications
Volume	67
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2020.101715
Publication status	Published - Oct 2020
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to thank the anonymous referee for their interesting and useful comments which permitted to improve the paper. The research of M. Bonini was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA INdAM ). The results showed in this paper are included in M. Bonini's Ph.D. thesis (supervised by the second author and G. Rinaldo).

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

AG Code
Norm-trace curve
Weight distribution

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10.1016/j.ffa.2020.101715

Intersections_Norm_Trace_and_ParabolasAccepted author manuscript, 574 KBLicence: CC BY-NC-ND 4.0

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title = "Intersections between the norm-trace curve and some low degree curves",

abstract = "In this paper we analyze the intersection between the norm-trace curve over Fq3 and the curves of the form y=ax3+bx2+cx+d, giving a complete characterization of the intersection between the curve and the parabolas (a=0), as well as sharp bounds for the other cases. This information is used for the determination of the weight distribution of some one-point AG codes arising from the curve.",

keywords = "AG Code, Norm-trace curve, Weight distribution",

author = "Matteo Bonini and Massimiliano Sala",

note = "Funding Information: The authors would like to thank the anonymous referee for their interesting and useful comments which permitted to improve the paper. The research of M. Bonini was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA INdAM ). The results showed in this paper are included in M. Bonini's Ph.D. thesis (supervised by the second author and G. Rinaldo). Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.ffa.2020.101715",

language = "English",

volume = "67",

journal = "Finite Fields and Their Applications",

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AU - Bonini, Matteo

AU - Sala, Massimiliano

N1 - Funding Information: The authors would like to thank the anonymous referee for their interesting and useful comments which permitted to improve the paper. The research of M. Bonini was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA INdAM ). The results showed in this paper are included in M. Bonini's Ph.D. thesis (supervised by the second author and G. Rinaldo). Publisher Copyright: © 2020 Elsevier Inc.

PY - 2020/10

Y1 - 2020/10

N2 - In this paper we analyze the intersection between the norm-trace curve over Fq3 and the curves of the form y=ax3+bx2+cx+d, giving a complete characterization of the intersection between the curve and the parabolas (a=0), as well as sharp bounds for the other cases. This information is used for the determination of the weight distribution of some one-point AG codes arising from the curve.

AB - In this paper we analyze the intersection between the norm-trace curve over Fq3 and the curves of the form y=ax3+bx2+cx+d, giving a complete characterization of the intersection between the curve and the parabolas (a=0), as well as sharp bounds for the other cases. This information is used for the determination of the weight distribution of some one-point AG codes arising from the curve.

KW - AG Code

KW - Norm-trace curve

KW - Weight distribution

UR - https://www.scopus.com/pages/publications/85089883097

U2 - 10.1016/j.ffa.2020.101715

DO - 10.1016/j.ffa.2020.101715

M3 - Journal article

AN - SCOPUS:85089883097

SN - 1071-5797

VL - 67

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

M1 - 101715

ER -

Intersections between the norm-trace curve and some low degree curves

Abstract

Bibliographical note

Keywords

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