A zero-dimensional approach to Hermitian codes

Edoardo Ballico; Alberto Ravagnani

doi:10.1016/j.jpaa.2014.05.031

A zero-dimensional approach to Hermitian codes

Edoardo Ballico
, Alberto Ravagnani

Mathematical Communication Theory

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

3 Citaten (Scopus)

Samenvatting

We study the algebraic geometry of a family of evaluation codes from plane smooth curves defined over any field. In particular, we provide a cohomological characterization of their dual minimum distance. After having discussed some general results on zero-dimensional subschemes of the plane, we focus on the interesting case of Hermitian s-point codes, describing the geometry of their dual minimum-weight codewords.

Originele taal-2	Engels
Pagina's (van-tot)	1031-1044
Aantal pagina's	14
Tijdschrift	Journal of Pure and Applied Algebra
Volume	219
Nummer van het tijdschrift	4
DOI's	https://doi.org/10.1016/j.jpaa.2014.05.031
Status	Gepubliceerd - 1 apr. 2015

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10.1016/j.jpaa.2014.05.031

https://arxiv.org/abs/1202.0894

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AB - We study the algebraic geometry of a family of evaluation codes from plane smooth curves defined over any field. In particular, we provide a cohomological characterization of their dual minimum distance. After having discussed some general results on zero-dimensional subschemes of the plane, we focus on the interesting case of Hermitian s-point codes, describing the geometry of their dual minimum-weight codewords.

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A zero-dimensional approach to Hermitian codes

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