On the Successive Minima of Subbases of Low-Dimensional Lattices

• 作者: Feng Gao Shikui Shang
• 来源期刊: 代数集刊:英文版
• 学科: 物理学
• 关键词: 晶格 最小值 接线板 低维 最优长度 中小企业 SMB 基础
• 年，卷（期）: 2014,（3）
• 页码范围: 477-482
• 页数: 6页
• 分类号: O731
• 语种: 中文

摘要

In this paper we discuss the global optimality of vector lengths for lattice bases. By introducing a partial order on lattice bases and the concept of successive minimal basis (SMB for short), we show that any of its minimal elements is a general greedy-reduced basis, and its least element (if exists) is an SMB. Furthermore, we prove the existence of SMB for lattices of dimension up to 6.