Abstract
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.
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The author would like to thank the referees for a lot of helpful comments.
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Communicated by J.-L. Kim.
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Han, S. A method for constructing self-dual codes over \(\mathbb {Z}_{2^m}\) . Des. Codes Cryptogr. 75, 253–262 (2015). https://doi.org/10.1007/s10623-013-9907-3
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DOI: https://doi.org/10.1007/s10623-013-9907-3