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

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	2946-2970
Number of pages	25
Journal	SIAM Journal on Discrete Mathematics
Volume	35
Issue number	4
DOIs	https://doi.org/10.1137/20M1356658
State	Published - 2021
Externally published	Yes

Keywords

PMDS codes
algebraic geometric codes
locally repairable codes
reducible curves

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10.1137/20M1356658

Cite this

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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 - Neri, Alessandro

AU - Velasco, Mauricio

PY - 2021

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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

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CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES

Abstract

Keywords

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