# On distances in lattices from algebraic number fields

## TL;DR

This paper investigates lattice constructions from algebraic number fields, introducing a new measure to analyze their properties, and provides exact calculations of minimum distances for certain fields with few complex embeddings.

## Contribution

It introduces a novel measure of algebraic numbers and derives exact minimum distances for lattices from number fields with limited complex embeddings.

## Key findings

- Exact minimum distances computed for specific number fields.
- New measure of algebraic numbers enhances lattice analysis.
- Lattices from fields with few complex embeddings have predictable properties.

## Abstract

In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we show that when the number fields have few complex embeddings, the minimum distances of these lattices can be computed exactly.