TY  - JOUR
TT  - No MacWilliams duality for codes over nonabelian groups
AU  - Julian Jr., M. Ryan
PY  - 2018
DA  - January
DO  - 10.13069/jacodesmath.369864
JF  - Journal of Algebra Combinatorics Discrete Structures and Applications
PB  - iPeak Academy
WT  - DergiPark
SN  - 2148-838X
SP  - 45
EP  - 49
VL  - 5
IS  - 1
KW  - Dual code
KW  - Subgroup lattice
KW  - MacWilliams identity
KW  - Iwasawa group
N2  - 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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UR  - https://doi.org/10.13069/jacodesmath.369864
L1  - https://dergipark.org.tr/tr/download/article-file/389000
ER  -