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In this article, we study negacyclic self-dual codes of length n over a finite chain ring R when the characteristic p of the residue field
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R
and the length n are relatively prime. We give necessary and sufficient conditions for the existence of (nontrivial) negacyclic self-dual codes over a finite chain ring. As an application, we construct negacyclic MDR self-dual codes over GR(p t , m) of length p m + 1.
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