On a duality for codes over non-abelian groups

Heiko Dietrich, Jeroen Schillewaert

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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.
Original languageEnglish
Pages (from-to)789-805
Number of pages17
JournalDesigns Codes and Cryptography
Issue number5
Publication statusPublished - May 2020


  • Group codes
  • Duality
  • Group lattice
  • Nilpotent groups

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