Linear label code of a root lattice using Gröbner bases
Pages 3 - 15
Abstract
The label code of a lattice plays a key role in the characterization of the lattice. Every lattice can be described in terms of a label code L and an orthogonal sublattice such that . 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 . As an application of the relation , where and denote binomial ideals associated to and L, respectively, a linear label code of is obtained using its Gröbner basis.
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Publication History
Published: 28 July 2023
Accepted: 13 June 2023
Revision received: 14 May 2023
Received: 14 October 2022
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- the Natural Sciences and Engineering Research Council of Canada
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