TY - JOUR

T1 - On a duality for codes over non-abelian groups

AU - Dietrich, Heiko

AU - Schillewaert, Jeroen

PY - 2020/5

Y1 - 2020/5

N2 - This work is motivated by a well-known open problem in coding theory, asking whether there is a duality theory for codes over non-abelian groups, see Dougherty et al. (Contemp Math 634:79–99, 2015). We prove that such a duality cannot be induced by a duality of a group lattice, and then study a variation that reduces to a group theoretic investigation: We say a finite group of order m has a layer-symmetric lattice if for every divisor d of m there is a bijection between the subgroups of order d and the subgroups of order m/d. We prove that every such group is nilpotent, and then investigate the class of finite p-groups with a layer-symmetric lattice.

AB - This work is motivated by a well-known open problem in coding theory, asking whether there is a duality theory for codes over non-abelian groups, see Dougherty et al. (Contemp Math 634:79–99, 2015). We prove that such a duality cannot be induced by a duality of a group lattice, and then study a variation that reduces to a group theoretic investigation: We say a finite group of order m has a layer-symmetric lattice if for every divisor d of m there is a bijection between the subgroups of order d and the subgroups of order m/d. We prove that every such group is nilpotent, and then investigate the class of finite p-groups with a layer-symmetric lattice.

KW - Group codes

KW - Duality

KW - Group lattice

KW - Nilpotent groups

UR - http://www.scopus.com/inward/record.url?scp=85077723330&partnerID=8YFLogxK

U2 - 10.1007/s10623-019-00711-z

DO - 10.1007/s10623-019-00711-z

M3 - Article

AN - SCOPUS:85077723330

VL - 88

SP - 789

EP - 805

JO - Designs Codes and Cryptography

JF - Designs Codes and Cryptography

SN - 0925-1022

IS - 5

ER -