We consider the use of linear constellation precoding and linear equalization in a multicarrier system to obtain improved performance over multipath fading channels at a low complexity. We split the full set of subcarriers into smaller groups and spread the data symbols assigned to each group via precoding matrices. To obtain diversity order gains at a given data rate, we derive the optimal split of the subcarriers (optimal grouping) and the optimal number of symbols assigned to each group (optimal loading) using a diversity-multiplexing tradeoff analysis. We also derive the necessary and sufficient optimality conditions for the precoder design and provide examples of such optimal precoders.