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On the P-construction of algebraic-geometry codes.

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Title: On the P-construction of algebraic-geometry codes.
Authors: Toledano, R.1,2 (AUTHOR) ridatole@gmail.com, Vides, M.1,2 (AUTHOR)
Source: Finite Fields & Their Applications. Aug2024, Vol. 97, pN.PAG-N.PAG. 1p.
Subjects: Hilbert functions, Finite fields, Projective spaces, Set functions, Point set theory, Sheaf theory
Abstract: We construct algebraic-geometry codes by using projective systems from projective curves over a finite field and the global sections of invertible sheaves on these curves. We also prove a formula for the Hilbert function of a finite set of points in a projective space in terms of the rank of a matrix constructed with the Veronese embedding and we use it to estimate the minimum distance of the dual codes. [ABSTRACT FROM AUTHOR]
Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 177757839
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: On the P-construction of algebraic-geometry codes.
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  Data: <searchLink fieldCode="AR" term="%22Toledano%2C+R%2E%22">Toledano, R.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> ridatole@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Vides%2C+M%2E%22">Vides, M.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Finite+Fields+%26+Their+Applications%22">Finite Fields & Their Applications</searchLink>. Aug2024, Vol. 97, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Hilbert+functions%22">Hilbert functions</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink><br /><searchLink fieldCode="DE" term="%22Projective+spaces%22">Projective spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Set+functions%22">Set functions</searchLink><br /><searchLink fieldCode="DE" term="%22Point+set+theory%22">Point set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Sheaf+theory%22">Sheaf theory</searchLink>
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  Label: Abstract
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  Data: We construct algebraic-geometry codes by using projective systems from projective curves over a finite field and the global sections of invertible sheaves on these curves. We also prove a formula for the Hilbert function of a finite set of points in a projective space in terms of the rank of a matrix constructed with the Veronese embedding and we use it to estimate the minimum distance of the dual codes. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.ffa.2024.102448
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Hilbert functions
        Type: general
      – SubjectFull: Finite fields
        Type: general
      – SubjectFull: Projective spaces
        Type: general
      – SubjectFull: Set functions
        Type: general
      – SubjectFull: Point set theory
        Type: general
      – SubjectFull: Sheaf theory
        Type: general
    Titles:
      – TitleFull: On the P-construction of algebraic-geometry codes.
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            NameFull: Toledano, R.
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            NameFull: Vides, M.
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              M: 08
              Text: Aug2024
              Type: published
              Y: 2024
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              Value: 97
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            – TitleFull: Finite Fields & Their Applications
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