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Construction of storage codes of rate approaching one on triangle-free graphs

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Abstract

Consider an assignment of bits to the vertices of a connected graph \(\Gamma (V, E)\) with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a storage code of length |V| on \(\Gamma \). In this paper we construct an infinite family of linear storage codes on triangle-free graphs with rates arbitrarily close to one.

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Acknowledgements

While we are finishing writing up this paper, we became aware of [1], in which the authors construct a family of storage codes of rate asymptotically one. Since both the construction in the current paper and the construction in [1] are generalizing the Hamming family, they look similar. However the methods used to compute the rates of storage codes are very different.

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Authors and Affiliations

  1. Department of Mathematics and National Center for Applied Mathematics Shenzhen, Southern University of Science and Technology, Shenzhen, 518055, China

    Hexiang Huang

  2. Department of Mathematics and Shenzhen International Center of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China

    Qing Xiang

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  1. Hexiang Huang
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  2. Qing Xiang
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Correspondence to Qing Xiang.

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Communicated by T. Feng

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Research partially supported by the National Natural Science Foundation of China grant 12071206, 12131011, 12150710510, and the Sino-German Mobility Programme M-0157.

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Huang, H., Xiang, Q. Construction of storage codes of rate approaching one on triangle-free graphs. Des. Codes Cryptogr. 91, 3901–3913 (2023). https://doi.org/10.1007/s10623-023-01278-6

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  • DOI: https://doi.org/10.1007/s10623-023-01278-6

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