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Families of Equiangular Lines and Lattices

Jacques Martinet

Abstract

We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related problems, and answer a question raised by Greaves ([G], Subsection~1.3.2).

Families of Equiangular Lines and Lattices

Abstract

We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related problems, and answer a question raised by Greaves ([G], Subsection~1.3.2).
Paper Structure (6 sections, 1 equation)

This paper contains 6 sections, 1 equation.

Table of Contents

  1. Basic Results
  2. Root Lattices and their duals
  3. Lattices of minimum 4 and 5
  4. A 13-Dimensional Lattice
  5. Lattices from the Leech Lattice
  6. Beyond dimension 23

Theorems & Definitions (9)

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