We have demonstrated a novel coherent optical detection architecture that serves as a matched filter and successfully discriminates between various encoded optical waveforms with high confidence. The waveforms are produced by encoding the spectral phase of an optical frequency comb with codes from a Walsh-Hadamard set. The encoded optical waveforms are decoded with a coherent detection technique implemented using an optical frequency comb as a set of local oscillators, an interferometer, and a pair of differential balanced photodetectors. The use of only linear optical devices in the receiver results in a higher sensitivity compared to the use of nonlinear optical thresholding and gating techniques. Decoding is demonstrated at power levels of ~ 25 μW, which are much lower than previously reported. Possible applications of the receiver architecture include laser radar and optical communications in an optical code-division multiple access network.