Decoding Sparse Reed-Solomon Codes with Known Support

Motivated by the use of trace codes in low-bandwidth repair, we investigate the decoding of a Reed-Solomon subcode whose information polynomials are characterized by a known sparse support. We ask: Can we correct more errors by leveraging the known structure of the information polynomial? We affirmatively respond to this query by introducing two schemes designed to complement any Reed-Solomon decoder. Our findings demonstrate better error-correcting capabilities than the naive way to decode based on the maximum degree of the information polynomial.