Dualities for finite abelian groups and applications to coding theory

preprint2026arXivOpen access

Abstract

The choice of an isomorphism, a duality, between a finite abelian group AA and its character group allows one to define dual codes of additive codes over AA. Properties of dualities and dual codes are studied, continuing work of Delsarte from 1973 and more recent work of Dougherty and his collaborators.

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