Construction of some perfect integral lattices with minimum 4

2014/01/15 by Roland Bacher, Bacher, Roland
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1401.3601

Final version, to appear in Journal de Th{é}orie des Nombres de Bordeaux

openalex publication_date 2014/01/15 · arxiv created 2015/10/19 · arxiv updated 2015/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct several families of perfect sublattices with minimum 4 of \mathbb Z^d. In particular, the number of d-dimensional perfect integral lattices with minimum 4 grows faster than d^k for every exponent k.

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