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Computer Science > Information Theory

arXiv:2303.16879 (cs)
[Submitted on 29 Mar 2023 (v1), last revised 3 Sep 2023 (this version, v5)]

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

Authors:Franciele do Carmo Silva, Ana Paula de Souza, Eleonesio Strey, Sueli I. R. Costa
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Abstract: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.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:2303.16879 [cs.IT]
  (or arXiv:2303.16879v5 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2303.16879
Journal reference: Communications in Mathematics, Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications) (September 10, 2023) cm:11146
Related DOI: https://doi.org/10.46298/cm.11146

Submission history

From: Franciele Silva [view email]
[v1] Wed, 29 Mar 2023 17:36:19 UTC (173 KB)
[v2] Fri, 31 Mar 2023 13:51:37 UTC (172 KB)
[v3] Fri, 11 Aug 2023 19:52:35 UTC (188 KB)
[v4] Mon, 28 Aug 2023 13:36:04 UTC (188 KB)
[v5] Sun, 3 Sep 2023 16:02:54 UTC (507 KB)
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