Fast Decoding of the p-Ary First-Order Reed-Muller Codes Based on Jacket Transform

Abstract

We propose a fast decoding algorithm for the p-ary first-order Reed-Muller code guaranteeing correction of up to [n/4sin(p-1/2pπ)] errors and having complexity proportional to nlogn, where n=p^m is the code length and p is an odd prime. This algorithm is an extension in the complex domain of the fast Hadamard transform decoding algorithm applicable to the binary case.