A tradeoff between the sub-packetization size and the repair bandwidth for reed-solomon code

Reed-Solomon (RS) codes are widely used in practical storage systems but their repair bandwidth characterization is still an open problem. RS codes can be viewed as the evaluations of a polynomial over a finite field. Recently, Guruswami and Wootters proposed a repair method for RS codes when the evaluation points are the entire field. Tamo, Ye and Barg achieved the minimum storage regenerating (MSR) bound when the sub-packetization size grows faster than the exponential function of the size of the evaluation points. In this work, we extend these results to accommodate different sizes of the evaluation points. Our schemes provide a flexible tradeoff between the sub-packetization size and the repair bandwidth. In addition, we present a technique for the sub-packetization bound of scalar MSR codes, based on the dimension of some constructed vector space.