2020/02/26 by Miezaki, Tsuyoshi, Munemasa, Akihiro, Nakasora, Hiroyuki · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Primary 94B05 #Secondary 05B05
paper · doi:10.48550/arxiv.2002.11353
In the present paper, we give Assmus--Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m with minimum norm 2m provides a spherical 3-design. We remark that some of such codes and lattices give t-designs for higher t. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24m with minimum weight 4m. Ternary and quaternary analogues are also given.