Lifted Reed-Solomon Codes with Application to Batch Codes [article]

Lukas Holzbaur and Rina Polyanskaya and Nikita Polyanskii and Ilya Vorobyev
2020 arXiv   pre-print
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
more » ... distributed storage systems. First, we improve the estimate of the code rate of lifted RS codes for lifting parameter m> 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.
arXiv:2001.11981v2 fatcat:fgvxlkcwkjbxrizmtiht4t4yci