An Introduction to Algebraic Geometry Codes

Munuera, Carlos; Olaya-León, Wilson

doi:10.1090/conm/642/12882

Cited by 3 publications

(2 citation statements)

References 36 publications

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“…Since the codes we study in this article are subcodes of Algebraic Geometry (AG) codes, we begin with a short reminder of this theory. For a complete reference on AG codes we address the reader to [11,16].…”

Section: Construction Of Lrc Codes From Curvesmentioning

confidence: 99%

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Locally recoverable codes from algebraic curves with separated variables

Munuera¹,

Tenório²,

Torres³

2020

Advances in Mathematics of Communications

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A Locally Recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. We study Locally Recoverable Algebraic Geometry codes arising from certain curves defined by equations with separated variables. The recovery of erasures is obtained by means of Lagrangian interpolation in general, and simply by one addition in some particular cases.2010 Mathematics Subject Classification. 94B27, 11G20, 11T71, 14G50, 94B05.

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Section: Construction Of Lrc Codes From Curvesmentioning

confidence: 99%

“…. The result follows from a straightforward computation using the well known fact that k * + d * ≥ n + 1 − g (see [11,Sect. 4.2]).…”

Section: 3mentioning

confidence: 99%

Locally recoverable codes from algebraic curves with separated variables

Munuera¹,

Tenório²,

Torres³

2020

Advances in Mathematics of Communications

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Quantum error-correcting codes from algebraic geometry codes of Castle type

Munuera

Tenório

Torres

2016

Quantum Inf Process

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Ideals of Numerical Semigroups and Error-Correcting Codes

Bras-Amorós

2019

Symmetry

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Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

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An Introduction to Algebraic Geometry Codes

Abstract: Abstract. We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.

Cited by 3 publications

References 36 publications

Locally recoverable codes from algebraic curves with separated variables

Locally recoverable codes from algebraic curves with separated variables

Quantum error-correcting codes from algebraic geometry codes of Castle type

Ideals of Numerical Semigroups and Error-Correcting Codes

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