Lifted Reed-Solomon Codes with Application to Batch Codes
Abstract
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 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.
Cite
@article{arxiv.2001.11981,
title = {Lifted Reed-Solomon Codes with Application to Batch Codes},
author = {Lukas Holzbaur and Rina Polyanskaya and Nikita Polyanskii and Ilya Vorobyev},
journal= {arXiv preprint arXiv:2001.11981},
year = {2020}
}
Comments
7 pages, 1 figure, a short version was submitted to ISIT 2020