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