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The second minimum of Barnes-Wall lattices

Gabriele Nebe

Abstract

We show that the second minimum of the Barnes-Wall lattices is a least $3/2$ of the minimum.

The second minimum of Barnes-Wall lattices

Abstract

We show that the second minimum of the Barnes-Wall lattices is a least of the minimum.
Paper Structure (6 sections, 6 theorems, 20 equations)

This paper contains 6 sections, 6 theorems, 20 equations.

Table of Contents

  1. Introduction
  2. The two Barnes-Wall lattices of dimension $2^m$
  3. The second minimum of the lattices $\Lambda_m$.
  4. The minimal classes in $\Lambda_m/\Delta _m$
  5. A recursive construction of $\Lambda _m$ as a subdirect product
  6. The main result

Key Result

Proposition 2.2

Theorems & Definitions (9)

  • Definition 2.1
  • Proposition 2.2
  • Theorem 2.3
  • Remark 2.4
  • Theorem 2.5
  • Lemma 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Remark 3.4