Rationality of the inner products of spherical s-distance t-designs for t≧2s-2, s≧3
Rationality of the inner products of spherical s-distance t-designs for t≧2s-2, s≧3
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t≧2s-2、s≧3 的球面 s 距离 t 设计内积的合理性
DOI：
10.1016/j.laa.2022.03.028
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发表时间：
2022
影响因子：
1.1
通讯作者：
Safaei Navid
中科院分区：
文献类型：
--
作者：
Boyvalenkov Peter;Nozaki Hiroshi;Safaei Navid
证明了球面S距离t设计的t≥2、S−2(Delsarte码)和S≥3的内积是有理的，唯一的例外是二十面体.在其他公式中，我们证明了除二十面体外，所有尖锐构型都有有理内积，所有达到Levenshtein界的球形码都有有理内积。
We prove that the inner products of spherical s-distance t-designs with t≥ 2 s− 2 (Delsarte codes) and s≥ 3 are rational with the only exception being the icosahedron. In other formulations, we prove that all sharp configurations have rational inner products and all spherical codes which attain the Levenshtein bound, have rational inner products, except for the icosahedron.