An improved list decoding algorithm for the second order Reed–Muller codes and its applications

We propose an algorithm which is an improved version of the Kabatiansky–Tavernier list decoding algorithm for the second order Reed–Muller code RM(2, m ), of length n = 2 m , and we analyse its theoretical and practical complexity. This improvement allows a better theoretical complexity. Moreover, we conjecture another complexity which corresponds to the results of our simulations. This algorithm has the strong property of being deterministic and this fact drives us to consider some applications, like determining some lower bounds concerning the covering radius of the RM(2, m ) code.