Dense packings from algebraic number fields and codes

DOI10.1016/j.ffa.2016.12.006zbMath1392.11046arXiv1506.00419OpenAlexW2243761002MaRDI QIDQ2396759

Shantian Cheng

Publication date: 24 May 2017

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00419

zbMATH Keywords

number fieldscodesdense packingsMinkowski lattice

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Algebraic numbers; rings of algebraic integers (11R04) Relations with coding theory (11H71)

Uses Software

• Magma
• Code Tables

Cites Work

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• A lower bound on packing density
• Applications of coding theory to the construction of modular lattices
• The Magma algebra system. I: The user language
• Sphere packings. (Edited by John Talbot)
• On the construction of dense lattices with a given automorphisms group
• An introduction to the geometry of numbers.
• Hermite’s Constant and Lattice Algorithms
• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results

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