Linear label code of a root lattice using Gröbner bases
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.
Applicable Algebra in Engineering, Communications and Computing
Aliasgari, Malihe; Panario, Daniel; and Sadeghi, Mohammad Reza, "Linear label code of a root lattice using Gröbner bases" (2023). Kean Publications. 330.