On the maximum number of vectors in $\{0,\pm 1{\}}^n$ with forbidden inner products

Abstract

Let $M\subset \{0,\pm 1{\}}^n$ be a set such that $(m,m)=4$ for every $m\in M$, and $(m_1,m_2)\in \{-4,-3,-2,-1,0,3\}$ for any two distinct vectors $m_1,m_2\in M$. We determine the maximum possible cardinality of such a set $M$ for all sufficiently large $n$.