Summary: Conway and Sloane have developed an efficient approach to the maximum- likelihood decoding of a linear block code based on the partitioning of the code into a subcode and its cosets. This procedure works for certain nonlinear codes as well, and we apply it in this paper to the development of several decoding algorithms for the extended Nordstrom-Robinson code used in conjunction with both BPSK and QPSK modulations. The small operation counts and the highly regular structures of many of these algorithms make them particularly well-suited to VLSI implementation. We describe one such implementation in this paper.