Constructing self-dual codes over \(\mathbb{F }_q[u]/(u^t)\)

Given a self-dual code over \(\mathbb{F }_q[u]/(u^t)\) we present a method to obtain explicitly new self-dual codes of larger length. Conversely, we also prove that, with the appropriate assumptions on length and number of generators, every self-dual code over \(\mathbb{F }_q[u]/(u^t)\) can be obtained in this manner. We use this construction to produce several optimal self-dual codes over the base field in a manner that generalizes the Lee weight. This construction is based on ideas presented by Han et al. (Bull Korean Math Soc, 49:135–143, 2012) and also by Lee and Kim (An efficient construction of self dual codes, 2012), not only generalizing it, but joining the two different cases from the original paper as special cases of one general construction.