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A new code aperture design framework for multiframe code aperture snapshot spectral imaging (CASSI) system is presented. It aims at the optimization of code aperture sets such that a group of compressive spectral measurements is constructed, each with information from a specific subset of bands. A matrix representation of CASSI is introduced that permits the optimization of spectrally selective code aperture sets. Furthermore, each code aperture set forms a matrix such that rank minimization is used to reduce the number of CASSI shots needed. Conditions for the code apertures are identified such that a restricted isometry property in the CASSI compressive measurements is satisfied with higher probability. Simulations show higher quality of spectral image reconstruction than that attained by systems using Hadamard or random code aperture sets.