A method for constructing self-dual codes over $$\mathbb {Z}_{2^m}$$ Z 2 m

There are several methods for constructing self-dual codes over various rings. Among them, the building-up method is a powerful method, and it can be applied to self-dual codes over finite fields and several rings. Recently, Alfaro and Dhul-Qarnayn (Des Codes Cryptogr, doi: 10.1007/s10623-013-9873-9 ) proposed a method for constructing self-dual codes over $${\mathbb F}_{q}[u]/(u^{t})$$ F q [ u ] / ( u t ) . Their approach is a building-up approach that uses the matrix form. In this paper, we use the matrix form to develop a building-up approach for constructing self-dual codes over $${\mathbb Z}_{2^m} (m \ge 1)$$ Z 2 m ( m ? 1 ) , which have not been considered thus far.