Polynomial techniques for investigation of spherical designs

Silvia Boumova; Peter Boyvalenkov; Hristina Kulina; Maya Stoyanova

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Polynomial techniques for investigation of spherical designs

机译：用于研究球形设计的多项式技术

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We investigate the structure of spherical r-designs by applying polynomial techniques for investigation of some inner products of such designs. Our approach can be used for large variety of parameters (dimension, cardinality, strength). We obtain new upper bounds for the largest inner product, lower bounds for the smallest inner product and some other bounds. Applications are shown for proving nonexistence results either in small dimensions and in certain asymptotic process. In particular, we complete the classification of the cardinalities for which 3-designs on S~(n-1) exist for n = 8, 13, 14 and 18. We also obtain new asymptotic lower bound on the minimum possible odd cardinality of 3-designs.

机译：我们通过应用多项式技术研究此类设计的一些内积，来研究球形r-设计的结构。我们的方法可用于多种参数（尺寸，基数，强度）。我们为最大的内积获得了新的上限，为最小的内积获得了下界以及其他一些界限。显示了用于证明小尺寸和某些渐近过程中不存在结果的应用。特别是，我们完成了对n = 8、13、14和18的S〜（n-1）上存在3个设计的基数的分类。我们还获得了3的最小可能奇数基数的新渐近下界设计。

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来源
《Designs, Codes and Crytography》 |2009年第3期|275-288|共14页
作者
Silvia Boumova; Peter Boyvalenkov; Hristina Kulina; Maya Stoyanova;
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作者单位

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,8 G. Bonchev Str., 1113 Sofia, Bulgaria;

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,8 G. Bonchev Str., 1113 Sofia, Bulgaria;

Faculty of Mathematics and Informatics. Plovdiv University,236 Bulgaria Blvd.. 4003 Plovdiv, Bulgaria;

Faculty of Mathematics and Informatics, Sofia University,5 James Baucher Blvd., 1164 Sofia, Bulgaria;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
spherical designs; polynomial techniques;

机译：球形设计;多项式技术;

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1. Polynomial techniques for investigation of spherical designs [J] . Silvia Boumova, Peter Boyvalenkov, Hristina Kulina, Designs, Codes and Cryptography . 2009,第3期

机译：用于研究球形设计的多项式技术
2. Polynomial designs II - Some existence results of exact rotatable spherical designs [J] . Bertrand F Comptes rendus. Mathematique . 2008,第23a24期

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3. On spherical designs obtained from Q-polynomial association schemes [J] . Suda S. Journal of combinatorial designs . 2011,第3期

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Polynomial techniques for investigation of spherical designs

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