Computational and Applied Mathematics

, Volume 37, Issue 3, pp 2413–2427 | Cite as

Bounds for the \(l_1\)-distance of q-ary lattices obtained via Constructions D, D\(^{'}\) and \(\overline{\text{ D }}\)

  • Eleonesio Strey
  • Sueli I. R. CostaEmail author


Lattices have been used in several problems in coding theory and cryptography. In this paper, we approach q-ary lattices obtained via Constructions D, \(\text{ D }'\) and \(\overline{\text{ D }}\). It is shown connections between Constructions D and \(\text{ D }'\). Bounds for the minimum \(l_1\)-distance of lattices \({\varLambda }_{D}\), \({\varLambda }_{D'}\) and \({\varLambda }_{\overline{D}}\) and, under certain conditions, a generator matrix for \({\varLambda }_{D'}\) are presented. In addition, when the chain of codes used is closed under the zero-one addition, we derive explicit expressions for the minimum \(l_1\)-distances of the lattices \({\varLambda }_{D}\) and \({\varLambda }_{\overline{D}}\) attached to the distances of the codes used in these constructions.


Lattices Lattices from q-ary codes Codes over rings \(l_1\)-distance Constructions D, D\('\) and \({\overline{\mathrm{D}}}\) 

Mathematics Subject Classification

94B05 06B99 52C99 



The authors are thankful to the reviewers for their comments and suggestions.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Department of Pure and Applied MathematicsFederal University of Espirito SantoAlegreBrazil
  2. 2.Institute of MathematicsUniversity of CampinasCampinasBrazil

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