Probabilistic decoders of Reed-Muller codes based on polynomial differentiation
N. S. Mogilevskaya · 2023
Several probabilistic decoders of second-order Reed-Muller codes are considered. These decoders share a common construction idea based on the differentiation of polynomials. The properties of these decoders are considered. It is shown that it is possible to modify these decoders for the case of any odd Galois field of cardinality more than 3, but it is theoretically impossible to justify the correctness of such algorithms.