Binary List Decoding Beyond Covering Radius

Wu\u2019s list decoding algorithm, when restricted to binary codes, allows decoding up to the binary Johnson bound. Unfortunately, in the vast majority of cases, this bound is not capable to reach the covering radius R of the code, and this implies that some n-tuples do exist that are not list decodable. Nevertheless we prove that a class of Reed-Muller codes it exists, for which the decoding radius Tau_wu is greater than or equal to the covering radius. This situation is the list decoding counterpart of perfect codes