In this paper, we study self-dual codes over commutative Artinian chain rings. Let R be such a ring, x be a generator of the unique maximal ideal of R and a∈N0\documentclass[12pt]{minimal}
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\begin{document}$$a\in {\mathbb {N}}_0 $$\end{document} maximal such that xa≠0\documentclass[12pt]{minimal}
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\begin{document}$$x^a\ne 0$$\end{document}. A code C over R of length t is an R-submodule of the free module Rt\documentclass[12pt]{minimal}
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\begin{document}$$R^t$$\end{document}. Multiplying powers of x to C defines the finite chain of subcodes C⊇C(1):=Cx⊇C(2):=Cx2⊇⋯⊇C(a):=Cxa⊇{0}.\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} C \supseteq C^{(1)} := C x \supseteq C^{(2)} := C x^2 \supseteq \dots \supseteq C^{(a)} := Cx^a \supseteq \lbrace 0 \rbrace . \end{aligned}$$\end{document}In this paper, we show that if C is a self-dual code in Rt\documentclass[12pt]{minimal}
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\begin{document}$$R^t$$\end{document}, then C(a)\documentclass[12pt]{minimal}
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\begin{document}$$C^{(a)}$$\end{document} is a (hermitian) self-dual code over the residue field F=R/⟨x⟩\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}= R / \langle x \rangle $$\end{document} if and only if C a free R-module (thus isomorphic to Rt2\documentclass[12pt]{minimal}
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\begin{document}$$R^{\frac{t}{2}}$$\end{document}). In this case, all codes C(i)\documentclass[12pt]{minimal}
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\begin{document}$$C^{(i)}$$\end{document} are self-dual codes in suitable bilinear or Hermitian spaces Wi\documentclass[12pt]{minimal}
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\begin{document}$$W_i$$\end{document} over F\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}$$\end{document} and we describe a method to construct all lifts C of a given self-dual code C(a)\documentclass[12pt]{minimal}
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\begin{document}$$C^{(a)}$$\end{document} over F\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}$$\end{document} that are self-dual, free codes over R. We apply this technique to codes over finite fields of characteristic p admitting an automorphism whose order is a power of p. For illustration, we show that the well-known Pless Code P36\documentclass[12pt]{minimal}
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\begin{document}$$P_{36}$$\end{document} is the only extremal, ternary code of length 36 with an automorphism of order 3, strengthening a result of Huffman, who showed the assertion for all prime orders ≥5\documentclass[12pt]{minimal}
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\begin{document}$$\ge 5$$\end{document}.
