Optimal codes as Tanner codes with cyclic component codes

Tom Høholdt; Fernando Piñero; Peng Zeng

doi:10.1007/s10623-014-9962-4

Optimal codes as Tanner codes with cyclic component codes

Tom Høholdt, Fernando Piñero, Peng Zeng^*

^*Corresponding author for this work

Software Engineering Institute

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

Abstract

In this article we study a class of graph codes with cyclic code component codes as affine variety codes. Within this class of Tanner codes we find some optimal binary codes. We use a particular subgraph of the point-line incidence plane of A(2, q) as the Tanner graph, and we are able to describe the codes succinctly using Gröbner bases.

Original language	English
Pages (from-to)	37-47
Number of pages	11
Journal	Designs, Codes, and Cryptography
Volume	76
Issue number	1
DOIs	https://doi.org/10.1007/s10623-014-9962-4
State	Published - 1 Jul 2015

Keywords

Affine variety codes
Expander codes
Graph based codes
Graph codes
Gröbner bases
Tanner codes

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10.1007/s10623-014-9962-4

Cite this

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title = "Optimal codes as Tanner codes with cyclic component codes",

abstract = "In this article we study a class of graph codes with cyclic code component codes as affine variety codes. Within this class of Tanner codes we find some optimal binary codes. We use a particular subgraph of the point-line incidence plane of A(2, q) as the Tanner graph, and we are able to describe the codes succinctly using Gr{\"o}bner bases.",

keywords = "Affine variety codes, Expander codes, Graph based codes, Graph codes, Gr{\"o}bner bases, Tanner codes",

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N2 - In this article we study a class of graph codes with cyclic code component codes as affine variety codes. Within this class of Tanner codes we find some optimal binary codes. We use a particular subgraph of the point-line incidence plane of A(2, q) as the Tanner graph, and we are able to describe the codes succinctly using Gröbner bases.

AB - In this article we study a class of graph codes with cyclic code component codes as affine variety codes. Within this class of Tanner codes we find some optimal binary codes. We use a particular subgraph of the point-line incidence plane of A(2, q) as the Tanner graph, and we are able to describe the codes succinctly using Gröbner bases.

KW - Affine variety codes

KW - Expander codes

KW - Graph based codes

KW - Graph codes

KW - Gröbner bases

KW - Tanner codes

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Optimal codes as Tanner codes with cyclic component codes

Abstract

Keywords

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