Reed-Muller-type codes over the segre variety

M. González-Sarabia; C. Rentería; H. Tapia-Recillas

doi:10.1006/ffta.2002.0360

Reed-Muller-type codes over the segre variety

M. González-Sarabia, C. Rentería, H. Tapia-Recillas

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

36 Citas (Scopus)

Resumen

The a-invariant is determined and a description of the defining ideal for the set S_K of rational points of the Segre variety over a finite field K is given. The dimension as well as the minimum distance of a Reed-Muller-type linear code defined over S_K are also determined. An example is given to illustrate the ideas.

Idioma original	Inglés
Páginas (desde-hasta)	511-518
Número de páginas	8
Publicación	Finite Fields and their Applications
Volumen	8
N.º	4
DOI	https://doi.org/10.1006/ffta.2002.0360
Estado	Publicada - oct. 2002

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title = "Reed-Muller-type codes over the segre variety",

abstract = "The a-invariant is determined and a description of the defining ideal for the set SK of rational points of the Segre variety over a finite field K is given. The dimension as well as the minimum distance of a Reed-Muller-type linear code defined over SK are also determined. An example is given to illustrate the ideas.",

keywords = "Defining ideal, Reed-Muller codes, Segre variety, a-invariant",

author = "M. Gonz{\'a}lez-Sarabia and C. Renter{\'i}a and H. Tapia-Recillas",

note = "Funding Information: 1Partially supported by COFAA-IPN and SNI-SEP, Me!xico. 2Partially supported by CONACyT and SNI-SEP, Me!xico.",

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AU - González-Sarabia, M.

AU - Rentería, C.

AU - Tapia-Recillas, H.

N1 - Funding Information: 1Partially supported by COFAA-IPN and SNI-SEP, Me!xico. 2Partially supported by CONACyT and SNI-SEP, Me!xico.

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N2 - The a-invariant is determined and a description of the defining ideal for the set SK of rational points of the Segre variety over a finite field K is given. The dimension as well as the minimum distance of a Reed-Muller-type linear code defined over SK are also determined. An example is given to illustrate the ideas.

AB - The a-invariant is determined and a description of the defining ideal for the set SK of rational points of the Segre variety over a finite field K is given. The dimension as well as the minimum distance of a Reed-Muller-type linear code defined over SK are also determined. An example is given to illustrate the ideas.

KW - Defining ideal

KW - Reed-Muller codes

KW - Segre variety

KW - a-invariant

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DO - 10.1006/ffta.2002.0360

M3 - Artículo

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JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

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Reed-Muller-type codes over the segre variety

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