In compressed sensing, the matrices that satisfy restricted isometry property (RIP) play an important role. But to date, very few results for designing such matrices are available. Of interest in several applications is a matrix whose elements are 0’s and 1’s (in short, 0; 1-matrix), excluding column normalization factors. Recently, DeVore (J Complexity 23:918–925, 2007) has constructed deterministic 0; 1-matrices that obey sparse recovery properties such as RIP. The present work extends the ideas embedded in DeVore (J Complexity 23:918–925, 2007) and shows that the 0; 1-matrices of different sizes can be constructed using multivariable homogeneous polynomials. © Springer International Publishing Switzerland 2016.