\indent the goal of this work is to describe principles for optimal encoding of multidimensional stimuli using neural populations. i will describe an analytic framework for finding maximally informative boundaries that separate stimuli according to combinations of neural responses. we find that for gaussian signals optimal decision boundaries are planar, regardless of neural noise level. for non-gaussian (or sparse) signals that are typical of our sensory environment, optimal decision boundaries are curved, and their shape depends both on the number of neurons in the network and on noise in individual neurons. finally, i will describe geometric properties of these decision boundaries that can be used as indicators of whether the network will be well described using pair-wise ising model, and if so, what are the values of the pairwise interactions.