CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES

Tristram Bogart; Anna Lena Horlemann-Trautmann; David Karpuk; Alessandro Neri; Mauricio Velasco

doi:10.1137/20M1356658

CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES

Tristram Bogart
, Anna Lena Horlemann-Trautmann
, David Karpuk
, Alessandro Neri
, Mauricio Velasco

Universidad de los Andes
University of St. Gallen
F-Secure Corporation
Technical University of Munich

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

3 Citas (Scopus)

Resumen

We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable codes geometrically. We obtain new general existence results, new explicit constructions, and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics, and probability theory.

Idioma original	Inglés
Páginas (desde-hasta)	2946-2970
Número de páginas	25
Publicación	SIAM Journal on Discrete Mathematics
Volumen	35
N.º	4
DOI	https://doi.org/10.1137/20M1356658
Estado	Publicada - 2021
Publicado de forma externa	Sí

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10.1137/20M1356658

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title = "CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES",

abstract = "We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable codes geometrically. We obtain new general existence results, new explicit constructions, and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics, and probability theory.",

keywords = "PMDS codes, algebraic geometric codes, locally repairable codes, reducible curves",

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AU - Bogart, Tristram

AU - Horlemann-Trautmann, Anna Lena

AU - Karpuk, David

AU - Neri, Alessandro

AU - Velasco, Mauricio

PY - 2021

Y1 - 2021

N2 - We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable codes geometrically. We obtain new general existence results, new explicit constructions, and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics, and probability theory.

AB - We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable codes geometrically. We obtain new general existence results, new explicit constructions, and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics, and probability theory.

KW - PMDS codes

KW - algebraic geometric codes

KW - locally repairable codes

KW - reducible curves

UR - https://www.scopus.com/pages/publications/85129980962

U2 - 10.1137/20M1356658

DO - 10.1137/20M1356658

M3 - Artículo

AN - SCOPUS:85129980962

SN - 0895-4801

VL - 35

SP - 2946

EP - 2970

JO - SIAM Journal on Discrete Mathematics

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IS - 4

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CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES

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