We define a self-dual code over a finite abelian group in terms of an arbitrary duality on the ambient space. We determine when additive self-dual codes exist over abelian groups for any duality and describe various constructions for these codes. We prove that there must exist self-dual codes under any duality for codes over a finite abelian group $${\mathbb {Z}}_{p^e}$$ . They exist for all lengths when p is prime and e is even; all even lengths when p is an odd prime with $$p \equiv 1 \pmod {4}$$ and e is odd with $$e>1$$ ; and all lengths that are $$0 \pmod {4}$$ when p is an odd prime with $$p \equiv 3 \pmod {4}$$ and e is odd with $$e>1.$$

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我们根据环境空间上的任意对偶性在有限阿贝尔群上定义自对偶码。我们确定任何对偶性的阿贝尔群上何时存在加性自对偶码，并描述这些码的各种构造。我们证明了在有限阿贝尔群 $${\mathbb {Z}}_{p^e}$$ 上的码的任何对偶性下一定存在自对偶码。当 p 为素数且 e 为偶数时，它们对所有长度都存在；当 p 是奇素数时的所有偶数长度 $$p \equiv 1 \pmod {4}$$ 并且 e 是奇数 $$e>1$$ ；以及所有长度为 $$0 \pmod {4}$$ 当 p 是奇质数且 $$p \equiv 3 \pmod {4}$$ 并且 e 是奇质数且 $$e>1.$$