A method for constructing self-dual codes over \(\mathbb {Z}_{2^m}\)
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 \({\mathbb F}_{q}[u]/(u^{t})\). 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 \({\mathbb Z}_{2^m} (m \ge 1)\), which have not been considered thus far.
self-dual code building-up construction \({\mathbb z}_{4}\) code \({\mathbb z}_{2^m}\) code 94b05 94b60