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

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

36 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	511-518
Number of pages	8
Journal	Finite Fields and their Applications
Volume	8
Issue number	4
DOIs	https://doi.org/10.1006/ffta.2002.0360
State	Published - Oct 2002

Keywords

Defining ideal
Reed-Muller codes
Segre variety
a-invariant

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10.1006/ffta.2002.0360

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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.",

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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 - Rentería, C.

AU - Tapia-Recillas, H.

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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

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ER -

Reed-Muller-type codes over the segre variety

Abstract

Keywords

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