Shadow lattices and shadow codes

Steven T. Dougherty, Masaaki Harada, Patrick Solé

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Recently shadows of unimodular lattices have been defined to derive upper bounds on the minimum norm of Type I lattices. In this paper we study shadows of lattices mostly to construct unimodular lattices in higher dimensions. We introduce shadow-optimal lattices which are a class of optimal Type I lattices by investigating theta series of optimal Type I lattices. These lattices are used to construct unimodular lattices by the above construction. An analogy between self-dual codes over the ring ℤ2k of integers and unimodular lattices is found. We also study shadow codes for Type I codes over ℤ2k by considering shadow lattices.

Original languageEnglish
Pages (from-to)49-64
Number of pages16
JournalDiscrete Mathematics
Volume219
Issue number1-3
DOIs
Publication statusPublished - 2000 May 28
Externally publishedYes

Keywords

  • Self-dual codes
  • Shadows
  • Unimodular lattices

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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