  In this paper, a construction of $(n,k,\delta)$ LDPC convolutional codes over
arbitrary finite fields, which generalizes the work of Robinson and Bernstein
and the later work of Tong is provided. The sets of integers forming a
$(k,w)$-(weak) difference triangle set are used as supports of some columns of
the sliding parity-check matrix of an $(n,k,\delta)$ convolutional code, where
$n\in\mathbb{N}$, $n>k$. The parameters of the convolutional code are related
to the parameters of the underlying difference triangle set. In particular, a
relation between the free distance of the code and $w$ is established as well
as a relation between the degree of the code and the scope of the difference
triangle set. Moreover, we show that some conditions on the weak difference
triangle set ensure that the Tanner graph associated to the sliding
parity-check matrix of the convolutional code is free from $2\ell$-cycles not
satisfying the full rank condition over any finite field. Finally, we relax
these conditions and provide a lower bound on the field size, depending on the
parity of $\ell$, that is sufficient to still avoid $2\ell$-cycles. This is
important for improving the performance of a code and avoiding the presence of
low-weight codewords and absorbing sets.
