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 binary Reed-Muller code RM(2, m), of length n = 2m , 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. Key words: list decoding, Reed-Muller codes, covering radius.

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Rafaël Fourquet, Cédric Tavernier
• Keywords: Better Theoretical Complexity, Computer Graphics, DCC 2008, List Decoding Algorithm, Practical Complexity