|Lifted Reed-Solomon Codes with Application to Batch Codes
|Lukas Holzbaur, Technical University of Munich, Germany; Rina Polyanskaya, Institute for Information Transmission Problems, Russia; Nikita Polyanskii, Technical University of Munich, Germany; Ilya Vorobyev, Skolkovo Institute of Science and Technology, Russia
|M.4: Codes for Distributed Storage IV
|Coding for Storage and Memories
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|Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring their restriction to every line in the space to be a codeword of the RS code. In this paper, we investigate lifted RS codes and discuss their application to batch codes, a notion introduced in the context of private information retrieval and load-balancing in distributed storage systems. First, we improve the estimate of the code rate of lifted RS codes for lifting parameter $m\ge 3$ and large field size. Second, a new explicit construction of batch codes utilizing lifted RS codes is proposed. For some parameter regimes, our codes have a better trade-off between parameters than previously known batch codes.