In this paper, we characterize the diversity properties of linear equalizers for block transmission systems, which unify preceded OFDM systems and zero-padded block transmissions. Fundamental results are proven to show that the diversity order of linear equalizers over fading channels can be the minimum (one) or the maximum diversity the channel offers. By exploiting the structure of the channel matrix, an alternative closed form expression for the pseudo-inverse is derived to reduce the complexity of the equalizer. Also, by quantifying the computational complexity, we demonstrate the complexity-performance tradeoff among the design for various linear equalizers. When the conditional error rate is known in closed form, a novel efficient approach is proposed to calculate the performance of linear zero-forcing equalizers. Corroborating simulations confirm that even with linear equalization, the block transmission systems perform better over channels with more taps at practical high SNRs.