Low dimensional strongly perfect lattices IV: The dual strongly perfect lattices of dimension 16

JOURNAL OF NUMBER THEORY

卷:208

Article

Hu, Sihuang^1,2  Nebe, Gabriele³ 

[1] Shandong Univ, Minist Educ, Key Lab Cryptol Technol & Informat Secur, Jinan, Shandong, Peoples R China

[2] Shandong Univ, Sch Cyber Sci & Technol, Jinan, Shandong, Peoples R China

[3] Rhein Westfal TH Aachen, Lehrstuhl Math, Aachen, Germany

关键词: Strongly perfect lattices;    Spherical designs;    Modular forms;    Locally densest lattices;   

DOI  :  10.1016/j.jnt.2019.08.001

来源: Elsevier

【 摘 要 】

We classify the dual strongly perfect lattices in dimension 16. There are four pairs of such lattices, the famous Barnes-Wall lattice Lambda(16), the extremal 5-modular lattice N-16, the odd Barnes-Wall lattice O-16 and its dual, and one pair of new lattices Gamma(16) and its dual. The latter pair belongs to a new infinite series of dual strongly perfect lattices, the sandwiched Barnes-Wall lattices, described by the authors in a previous paper. An updated table of all known strongly perfect lattices up to dimension 26 is available in the catalogue of lattices [15]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free