Year 2018, Volume 5 , Issue 1, Pages 45 - 49 2018-01-15

No MacWilliams duality for codes over nonabelian groups

M. Ryan Julian Jr. [1]


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 $n$.
Dual code, Subgroup lattice, MacWilliams identity, Iwasawa group
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Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-6117-1415
Author: M. Ryan Julian Jr.

Dates

Publication Date : January 15, 2018

Bibtex @research article { jacodesmath369864, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2018}, volume = {5}, pages = {45 - 49}, doi = {10.13069/jacodesmath.369864}, title = {No MacWilliams duality for codes over nonabelian groups}, key = {cite}, author = {Julian Jr., M. Ryan} }
APA Julian Jr., M . (2018). No MacWilliams duality for codes over nonabelian groups . Journal of Algebra Combinatorics Discrete Structures and Applications , 5 (1) , 45-49 . DOI: 10.13069/jacodesmath.369864
MLA Julian Jr., M . "No MacWilliams duality for codes over nonabelian groups" . Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 45-49 <https://dergipark.org.tr/en/pub/jacodesmath/issue/33304/369864>
Chicago Julian Jr., M . "No MacWilliams duality for codes over nonabelian groups". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 45-49
RIS TY - JOUR T1 - No MacWilliams duality for codes over nonabelian groups AU - M. Ryan Julian Jr. Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.369864 DO - 10.13069/jacodesmath.369864 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 45 EP - 49 VL - 5 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.369864 UR - https://doi.org/10.13069/jacodesmath.369864 Y2 - 2017 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications No MacWilliams duality for codes over nonabelian groups %A M. Ryan Julian Jr. %T No MacWilliams duality for codes over nonabelian groups %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 1 %R doi: 10.13069/jacodesmath.369864 %U 10.13069/jacodesmath.369864
ISNAD Julian Jr., M. Ryan . "No MacWilliams duality for codes over nonabelian groups". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 1 (January 2018): 45-49 . https://doi.org/10.13069/jacodesmath.369864
AMA Julian Jr. M . No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(1): 45-49.
Vancouver Julian Jr. M . No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(1): 45-49.