Lattices of type $A_n$, $D_n$, $E_n$ and codes

TL;DR

This paper introduces a generalized method for constructing lattices of types A, D, and E from codes, extending previous constructions and exploring applications to Hilbert modular forms.

Contribution

It generalizes the classical Construction A for lattices from p-ary codes to include types A, D, and E, and demonstrates applications to Hilbert modular forms.

Findings

Generalized lattice construction from codes for types A, D, E

Examples of applications to Hilbert modular forms

Extension of classical Construction A

Abstract

We propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$. This construction is a generalization of construction A of lattices from $p$-ary codes corresponding to a lattice of type $A_{p-1}$. Moreover, we introduce some examples of application of lattices from the construction to Hilbert modular form.