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Guo, Kopparty and Sudan have initiated the study of error-correcting codesderived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codesare defined as the evaluation of polynomials in a vector space over a field byrequiring their restriction to every line in the space to be a codeword of theRS code. In this paper, we investigate lifted RS codes and discuss theirapplication to batch codes, a notion introduced in the context of privateinformation retrieval and load-balancing in distributed storage systems. First,we improve the estimate of the code rate of lifted RS codes for liftingparameter $m\ge 3$ and large field size. Second, a new explicit construction ofbatch codes utilizing lifted RS codes is proposed. For some parameter regimes,our codes have a better trade-off between parameters than previously knownbatch codes.

Lifted Reed-Solomon Codes with Application to Batch Codes