Linear label code of a root lattice using Gröbner bases

Malihe Aliasgari, Daniel Panario, Mohammad Reza Sadeghi

Research output: Contribution to journalArticlepeer-review

Abstract

The label code of a lattice plays a key role in the characterization of the lattice. Every lattice Λ can be described in terms of a label code L and an orthogonal sublattice Λ such that Λ / Λ ≅ L . We identify the binomial ideal associated to an integer lattice and then establish a relation between the ideal quotient of the lattice and its label code. Furthermore, we present the Gröbner basis of the well-known root lattice Dn . As an application of the relation IΛ=IΛ′+IL , where IΛ,IΛ′ and IL denote binomial ideals associated to Λ,Λ′ and L, respectively, a linear label code of Dn is obtained using its Gröbner basis.

Original languageEnglish
Pages (from-to)3-15
Number of pages13
JournalApplicable Algebra in Engineering, Communications and Computing
Volume35
Issue number1
DOIs
StatePublished - Jan 2024

Keywords

  • Binomial ideal
  • Gröbner bases
  • Label code
  • Lattice

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