Decoding of Reed-Solomon codes for additive cost functions

Efficient list decoding of Reed-Solomon codes beyond their error-correction radius has been studied in a number of recent papers. The approach is based on algebraic weighted-interpolation techniques. In this paper, we develop weight assignment schemes for arbitrary additive cost functions. Such functions are defined on the product space F_q×𝒴 They include the Hamming metric and the generalized Hamming metric, as well as log-likelihood based costs, as special cases.