NEW NONEXISTENCE RESULTS FOR SPHERICAL DESIGNS

被引：0

作者：

Boyvalenkov, Peter ^{[1
,3
]}

Stoyanova, Maya ^{[2
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

[2] Univ Sofia, Fac Math & Informat, Sofia 1164, Bulgaria

[3] Southwestern Univ, Fac Math & Nat Sci, Dept Informat, Blagoevgrad 2700, Bulgaria

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2013年 / 7卷 / 03期

关键词：

Spherical designs; bounds for spherical designs;

D O I：

10.3934/amc.2013.7.279

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

New nonexistence results for spherical designs of odd strength and odd cardinality are proved by improvements on previously applied polynomial techniques. This implies new bounds on the designs under consideration either in small dimensions and in certain asymptotic process.

引用

页码：279 / 292

页数：14

共 11 条

[1]

Abramowitz M., 1964, HDB MATH FUNCTIONS, V55

[2] Spherical designs and generalized sum-free sets in abelian groups [J].

Bajnok, B .

DESIGNS CODES AND CRYPTOGRAPHY, 2000, 21 (1-3) :11-18

[3] A method for proving nonexistence of spherical designs of odd strength and odd cardinality [J].

Boumova, S. ;

Boyvalenkov, P. ;

Stoyanova, M. .

PROBLEMS OF INFORMATION TRANSMISSION, 2009, 45 (02) :110-123

[4]

BOUMOVA S., 2003, CONSTRUCTIVE THEORY, P225

[5]

Boumova S., 2002, P INT WORKSH ACCT SE, P54

[6] Polynomial techniques for investigation of spherical designs [J].

Boumova, Silvia ;

Boyvalenkov, Peter ;

Kulina, Hristina ;

Stoyanova, Maya .

DESIGNS CODES AND CRYPTOGRAPHY, 2009, 51 (03) :275-288

[7] Necessary conditions for existence of some designs in polynomial metric spaces [J].

Boyvalenkov, P ;

Boumova, S ;

Danev, D .

EUROPEAN JOURNAL OF COMBINATORICS, 1999, 20 (03) :213-225

[8] Nonexistence of certain spherical designs of odd strengths and cardinalities [J].

Boyvalenkov, P ;

Danev, D ;

Nikova, S .

DISCRETE & COMPUTATIONAL GEOMETRY, 1999, 21 (01) :143-156

[9] A new asymptotic bound of the minimum possible odd cardinality of spherical (2k-1)-designs [J].

Boyvalenkov, Peter ;

Stoyanova, Maya .

DISCRETE MATHEMATICS, 2010, 310 (15-16) :2170-2175

[10]

Delsarte P., 1977, Geometriae Dedicata, V6, P363, DOI [DOI 10.1007/BF03187604, 10.1007/BF03187604]

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