Bounds for the l₁-distance of q-ary lattices obtained via Constructions D, D^' and D

2016/11/02 by Strey, Eleonesio, Costa, Sueli I. R.
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1611.00435

Abstract

Lattices have been used in several problems in coding theory and cryptography. In this paper we approach q-ary lattices obtained via Constructions D, \D' and D. It is shown connections between Constructions D and \D'. Bounds for the minimum l₁-distance of lattices Λ_D, Λ_D' and Λ_D and, under certain conditions, a generator matrix for Λ_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 l₁-distances of the lattices Λ_D and Λ_D attached to the distances of the codes used in these constructions.

Related

• On q-ary codes with two distances d and d+1
• Lattices from codes over ℤ_q: Generalization of Constructions D, D' and D
• Bounds on Box Codes
• Antichain Codes
• Bounds on the minimum distance of locally recoverable codes