2009/10/11 by Robert L. Griess, Griess, Robert L.
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Number Theory (math.NT) #Primary 11H50 #Secondary 11H56 #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0910.2055
openalex publication_date 2009/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a polarization of an even unimodular lattice and integer k≥ 1, we define a family of unimodular lattices L(M,N,k). Of special interest are certain L(M,N,3) of rank 72. Their minimum norms lie in \4, 6, 8\. Norms 4 and 6 do occur. Consequently, 6 becomes the highest known minimum norm for rank 72 even unimodular lattices. We discuss how norm 8 might occur for such a L(M,N,3). We note a few L(M,N,k) in dimensions 96, 120 and 128 with moderately high minimum norms.