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Optimal codes as Tanner codes with cyclic component codes

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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 \(\mathbf {A}(2,q)\) as the Tanner graph, and we are able to describe the codes succinctly using Gröbner bases.

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Acknowledgments

The authors gratefully acknowledge the generous support from the Danish National Research Foundation and the National Science Foundation of China (Grant No. 11061130539) for the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography. The third author would also like to acknowledge the support of the National Natural Science Foundation of China under Grants Nos. 61321064 and 61103222 and the Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20110076120016.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark

    Tom Høholdt & Fernando Piñero

  2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, People’s Republic of China

    Peng Zeng

Authors
  1. Tom Høholdt
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  2. Fernando Piñero
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  3. Peng Zeng
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Corresponding author

Correspondence to Peng Zeng.

Additional information

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Computer Algebra in Coding Theory and Cryptography”.

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Høholdt, T., Piñero, F. & Zeng, P. Optimal codes as Tanner codes with cyclic component codes. Des. Codes Cryptogr. 76, 37–47 (2015). https://doi.org/10.1007/s10623-014-9962-4

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  • DOI: https://doi.org/10.1007/s10623-014-9962-4

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