No MacWilliams duality for codes over nonabelian groups
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 do...
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Format: | Article |
Language: | English |
Published: |
Yildiz Technical University
2017-12-01
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Series: | Journal of Algebra Combinatorics Discrete Structures and Applications |
Online Access: | http://jacodesmath.com/index.php/jacodesmath/article/view/117 |
Summary: | 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 $n$. |
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ISSN: | 2148-838X |