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In wireless communications, the fading multipath channel attenuates and distorts the transmitted signal. To decode the transmitted symbols and take advantage of the full multipath diversity that the channel has to offer, computationally complex maximum-likelihood (ML) decoding is often employed. We show that a linear equalizer followed by a hard decision is capable of benefiting from maximum multipath diversity in linearly precoded orthogonal frequency-division multiplexing (OFDM) systems, where the information symbols are mapped through a matrix transformation before the inverse fast Fourier transform (IFFT) at the OFDM transmitter. As far as we are aware, this is the first proof of a linear equalization scheme achieving maximum multipath diversity over single-input single-output wireless links. We can conclude from this result that at sufficiently high signal-to-noise ratios (SNR), precoded OFDM systems will perform better over channels with more taps even with linear equalization, due to the increase in diversity order.