No MacWilliams duality for codes over nonabelian groups

Abstract

Dougherty, Kim, and Sol\'e [3] have asked whether there is a duality theory and a MacWilliams formula for codes over nonabelian groups, or more generally, whether there is any subclass of nonabelian groups which have such a duality theory. We answer this in the negative by showing that there does not exist a nonabelian group $G$ with a duality theory on the subgroups of $G^n$ for all $n$.

Keywords

• Dual code,Subgroup lattice,MacWilliams identity,Iwasawa group

References

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