  In this paper, deterministic construction of measurement matrices in
Compressive Sensing (CS) is considered. First, by employing the column
replacement concept, a theorem for construction of large minimum distance
linear codes containing all-one codewords is proposed. Then, by applying an
existing theorem over these linear codes, deterministic sensing matrices are
constructed. To evaluate this procedure, two examples of constructed sensing
matrices are presented. The first example contains a matrix of size
${{p}^{2}}\times {{p}^{3}}$ and coherence ${1}/{p}\;$, and the second one
comprises a matrix with the size $p\left( p-1 \right)\times {{p}^{3}}$ and
coherence ${1}/{\left( p-1 \right)}\;$, where $p$ is a prime integer. Based on
the Welch bound, both examples asymptotically achieve optimal results.
Moreover, by presenting a new theorem, the column replacement is used for
resizing any sensing matrix to a greater-size sensing matrix whose coherence is
calculated. Then, using an example, the outperformance of the proposed method
is compared to a well-known method. Simulation results show the satisfying
performance of the column replacement method either in created or resized
sensing matrices.
