Linear label code of a root lattice using Gröbner bases

Document Type

Article

Publication Date

1-1-2023

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.

Publication Title

Applicable Algebra in Engineering, Communications and Computing

DOI

10.1007/s00200-023-00614-6

This document is currently not available here.

Share

COinS