Zero-divisor super-λ graphs

In coding theory, super-lambda graphs were used to build linear codes. Thus, in order to see whether the zero-divisor graphs might be useful into this context, it is natural to study when zero-divisor graphs of some non elementary ring constructions are super-lambda graphs. In this paper, using the finite direct product of finite fields, the ring of the residues, and the trivial extension of rings by a module, we show that there are various classes of rings whose zero-divisor graphs are super-lambda. We apply these results to determine parameters of some linear codes associated to zero-divisor graphs.