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Bounds on generalized FR codes using hypergraphs

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Abstract

In the Distributed Storage Systems (DSSs), the encoded fraction of information is stored in a distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes has been introduced, in which, encoded data information is stored on distributed servers using an encoding involving a Maximum Distance Separable (MDS) code and a Repetition code. In this work, we have considered FR codes with asymmetric parameters known as Generalized Fractional Repetition (GFR) codes. We have shown that any GFR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the associated GFR code. In general, using the correspondence, the necessary and sufficient conditions for the existence of a GFR code is obtained. It is also shown that any GFR code associated with a linear hypergraph is universally good, and any locally repairable GFR code is associated with a class of non-linear hypergraph.

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Authors and Affiliations

  1. Indian Institute of Technology Kanpur, Kanpur, India

    Krishna Gopal

  2. Dhirubhai Ambani Institute of Information and Communication Technology Gandhinagar, Gandhinagar, India

    Manish K. Gupta

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  1. Krishna Gopal
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  2. Manish K. Gupta
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Correspondence to Manish K. Gupta.

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The preliminary version of the paper is available at https://arxiv.org/abs/1711.07631.

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Gopal, K., Gupta, M.K. Bounds on generalized FR codes using hypergraphs. J. Appl. Math. Comput. 65, 771–792 (2021). https://doi.org/10.1007/s12190-020-01414-8

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