  In recent times, the construction of deterministic matrices has gained
popularity as an alternative of random matrices as they provide guarantees for
recovery of sparse signals. In particular, the construction of binary matrices
has attained significance due to their potential for hardware-friendly
implementation and appealing applications. Our present work aims at
constructing incoherent binary matrices consisting of orthogonal blocks with
small block coherence. We show that the binary matrices constructed from Euler
squares exhibit block orthogonality and possess low block coherence. With a
goal of obtaining better aspect ratios, the present work generalizes the notion
of Euler Squares and obtains a new class of deterministic binary matrices of
more general size. For realizing the stated objectives, to begin with, the
paper revisits the connection of finite field theory to Euler Squares and their
construction. Using the stated connection, the work proposes Generalized Euler
Squares (GES) and then presents a construction procedure. Binary matrices with
low coherence and general row-sizes are obtained, whose column size is in the
maximum possible order. Finally, the paper shows that the special structure
possessed by GES is helpful in resulting in block orthogonal structure with
small block coherence, which supports the recovery of block sparse signals.
