  We give a framework for generalizing LDPC code constructions that use
Transversal Designs or related structures such as mutually orthogonal Latin
squares. Our construction offers a broader range of code lengths and codes
rates. Similar earlier constructions rely on the existence of finite fields of
order a power of a prime. In contrast the LDPC codes constructed here are based
on difference matrices and difference covering arrays, structures available for
any order $a$. They satisfy the RC constraint and have, for $a$ odd, length
$a^2$ and rate $1-\frac{4a-3}{a^2}$, and for $a$ even, length $a^2-a$ and rate
at least $1-\frac{4a-6}{a^2-a}$. When $3$ does not divide $a$, these LDPC codes
have stopping distance at least $8$. When $a$ is odd and both $3$ and $5$ do
not divide $a$, our construction delivers an infinite family of QC-LDPC codes
with minimum distance at least $10$. The simplicity of the construction allows
us to theoretically verify these properties and analytically determine lower
bounds for the minimum distance and stopping distance of the code. The BER and
FER performance of our codes over AWGN (via simulation) is at the least
equivalent to codes constructed previously, while in some cases significantly
outperforming them.
