In this paper, the authors study the design of codes for Distributed Storage Systems (DSS) that enable local repair in the event of node failure. This paper presents locally repairable codes based on low degree multivariate polynomials. Its code construction mechanism extends work on noisy Interpolating Set by the researcher. The paper presents two classes of codes that allow node repair to be performed by contacting 2 and 3 surviving nodes respectively. It further shows that both classes are good in terms of their rate and minimum distance, and allow their rate to be bartered for greater flexibility in the repair process.