A Gilbert-Varshamov-type bound for lattice packings

作者：Xing Chaoping^*; Yeo Sze Ling

来源：Journal of Combinatorial Theory - Series A, 2011, 118(3): 938-948.

DOI：10.1016/j.jcta.2010.06.002

• Center density
• Number fields
• Theta series
• Rush's construction

A Gilbert-Varshamov-type bound for Euclidean packings was recently found by Nebe and Xing. In this present paper, we derive a Gilbert-Varshamov-type bound for lattice packings by generalizing Rush's approach of combining p-ary codes with the lattice pZ(n). Specifically, we will exploit suitable sublattices of Z(n) as well as lattices of number fields in our construction. Our approach allows us to compute the center densities of lattices of moderately large dimensions which compare favorably with the best known densities given in the literature as well as the densities derived directly via Rush's method.

• 出版日期2011-4
• 单位南阳理工学院