On optimal weight assignmnents for multivariate interpolation list-decoding

We consider the weight assignment problem for multivariate interpolation-based decoding. The resulting optimization problem is solved under the assumption that the codes are not too short (the integrality gap for our relaxations approaches zero as the code length grows) and the optimal weight assignment scheme is given for the criterion of maximizing an allowable additive cost (e.g. Hamming distance or log-probability, etc.) of an error event.