No MacWilliams duality for codes over nonabelian groups

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Michael Ryan Julian¹ 

[1] University of Wisconsin

关键词: Dual code;    Subgroup lattice;    MacWilliams identity;    Iwasawa group;   

DOI  :  10.13069/jacodesmath.369864

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Dougherty, Kim, and Solé [3] have asked whether there is a duality theory and a MacWilliams formulafor codes over nonabelian groups, or more generally, whether there is any subclass of nonabelian groupswhich have such a duality theory. We answer this in the negative by showing that there does notexist a nonabelian group G with a duality theory on the subgroups of Gnfor all n.

【 授权许可】

CC BY