Dualities for finite abelian groups and applications to coding theory

TL;DR

This paper explores dualities in finite abelian groups and their application to defining and analyzing dual codes in coding theory, building on foundational work by Delsarte and others.

Contribution

It introduces a framework for dualities in finite abelian groups and examines their properties and implications for additive codes in coding theory.

Findings

Characterizes properties of dualities and dual codes.

Extends Delsarte's work from 1973.

Provides new insights into additive code duality.

Abstract

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