Dougherty, Steven T.Korban, AdrianSahinkaya, Serap2025-03-172025-03-1720220938-12791432-0622https://doi.org/10.1007/s00200-020-00473-5https://hdl.handle.net/20.500.13099/2376We 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 Z(pe). They exist for all lengths when p is prime and e is even; all even lengths when p is an odd prime with p = 1 (mod 4) and e is odd with e > 1; and all lengths that are 0 (mod 4) when p is an odd prime with p = 3 (mod 4) and e is odd with e > 1.eninfo:eu-repo/semantics/closedAccessSelf-dual codesFinite abelian groupsGroup charactersSelf-dual additive codesArticle10.1007/s00200-020-00473-5335569586Q4WOS:0005911417000012-s2.0-85096379604Q1