Matrices With Small Coherence Using $p$-Ary Block Codes

In contrast to the vast amount of literature in random matrices in the field of compressed sensing, the subject of deterministic matrix design is at its early stages. Since these deterministic matrices are usually constructed using the polynomials in finite Galois fields, the number of rows (number of samples) is restricted to some specific integers such as prime powers. In this paper, besides extending a previous matrix design based on the binary BCH codes to the
p
-ary codes, we introduce matrices with wide variety of options for the number of rows. Simulation results demonstrate that these matrices perform almost as well as random matrices.