Recently, an important set of high dimensional signals (HDS) applications has successfully implemented compressive sensing (CS) sensors in which their efficiency depends on physical elements that perform a binary codification over the HDS. The structure of the binary codification is crucial as it determines the HDS sensing matrices. For a correct reconstruction, this class of matrices drastically differs from the dense or i.i.d. assumptions usually made in CS. Therefore, current CS matrix design algorithms are impractical. This paper proposes a novel strategy to design structured, sparse, and binary HDS measurement matrices based on promoting linear independence between rows by minimizing the number of its zero singular values. The design constraints lead to keep uniform both, the number of non-zero elements per row and also the number of non-zero elements per column. An algorithm based on an optimal selection of non-zero entries positions is developed to implement this strategy. Simulations show that the proposed optimization improves the quality of the reconstructed HDS in up to 8 dB of PSNR compared with non-optimized matrices.