In this paper we introduce deterministic $m\times n$ RIP fulfilling $\pm 1$matrices of order $k$ such that $\frac{\log m}{\log k}\approx \frac{\log(\log_2n)}{\log(\log_2 k)}$. The columns of these matrices are binary BCH code vectorsthat their zeros are replaced with -1 (excluding the normalization factor). Thesamples obtained by these matrices can be easily converted to the originalsparse signal; more precisely, for the noiseless samples, the simple MatchingPursuit technique, even with less than the common computational complexity,exactly reconstructs the sparse signal. In addition, using Devore's binarymatrices, we expand the binary scheme to matrices with $\{0,1,-1\}$ elements.
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