Algebraic List Decoding of Reed-Solomon product codes

The product code of two Reed-Solomon codes can be regarded as an evaluation codes of bivariate polynomials, whose degrees in each variable are bounded. We propose to decode these codes with a generalization of the Guruswami-Sudan interpolation-based list decoding algorithm. A relative decoding radius of 1 − 6 √4R is found, where is the rate of the product code. We also discuss a generalization to the M variables base, where we get a figure of 1 − M(M+1) √R. Finally the Pellikaan and Wu decoding algorithm is used to improve the decdoing radius.