On Almost Perfect Linear Lee Codes of Packing Radius 2

Xu, Xin-Shun; Zhou, Yue

doi:10.1109/tit.2023.3287222

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Cited by 4 publications

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“…Besides the Euclidean distance (P = 2), other L P -distances have been considered either theoretically, such as the search for perfect and quasi-perfect codes under P-Lee distance [12,74,51,72], or for applications in Cryptography and communications. Several works in lattice-based cryptography, for instance, analyze the complexity of certain computational problems related to lattices in the L P -norms, such as the closed and the shortest vector problems (CVP and SVP) [47] and the bounded decoding distance (BDD) [5].…”

Section: Minimum Distancementioning

confidence: 99%

On Lattice Constructions D and D' from q-ary Linear Codes

Silva,

de Souza,

Strey

et al. 2023

Communications in Mathematics

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Multilevel lattice codes, such as those associated to Constructions $C$, $\overline{D}$, D and D', have relevant applications in communications. In this paper, we investigate some properties of lattices obtained via Constructions D and D' from $q$-ary linear codes. Connections with Construction A, generator matrices, expressions and bounds for the lattice volume and minimum distances are derived. Extensions of previous results regarding construction and decoding of binary and $p$-ary linear codes ($p$ prime) are also presented.

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