论文标题
四点半限定的等缘线
Four-point semidefinite bound for equiangular lines
论文作者
论文摘要
$ \ mathbb {r}^d $中的一组线通过原点称为equiangular，如果集合中的两行形式相同。我们证明了由Bachoc和Vallentin开发的三点半限制约束的替代版本，以及Musin为球形代码开发的多点半限制约束。当相关对象是球形$ s $ distance集时，替代的半限制约束更为简单。使用替代性的四点半限制约束，我们发现了针对等角线的四点半菲尼斯结合。该结果改善了与规定角度无限多个维度$ d $的上限。作为绑定的必然性，我们证明了在$ \ mathbb {r}^d $中最大程度地构建等距线的独特性。
A set of lines in $\mathbb{R}^d$ passing through the origin is called equiangular if any two lines in the set form the same angle. We proved an alternative version of the three-point semidefinite constraints developed by Bachoc and Vallentin, and the multi-point semidefinite constraints developed by Musin for spherical codes. The alternative semidefinite constraints are simpler when the concerned object is a spherical $s$-distance set. Using the alternative four-point semidefinite constraints, we found the four-point semidefinite bound for equiangular lines. This result improves the upper bounds for infinitely many dimensions $d$ with prescribed angles. As a corollary of the bound, we proved the uniqueness of the maximum construction of equiangular lines in $\mathbb{R}^d$ for $7 \leq d \leq 14$ with inner product $α= 1/3$, and for $23 \leq d \leq 64$ with $α= 1/5$.
