G. Nebe, B. Venkov, “On tight spherical designs”, Algebra i Analiz, 24:3 (2012), 163–171; St. Petersburg Math. J., 24:3 (2013), 485

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Algebra i Analiz, 2012, Volume 24, Issue 3, Pages 163–171 (Mi aa1287)

This article is cited in 14 scientific papers (total in 14 papers)

Research Papers

On tight spherical designs

G. Nebe, B. Venkov

Lehrstuhl D für Mathematik, RWTH Aachen, Aachen, Germany

Full-text PDF (165 kB) Citations (14)

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Abstract: Let $X$ be a tight $t$-design of dimension $n$, and let $t=5$ or $t=7$ (the open cases). An investigation of the lattice generated by $X$ by using arithmetic theory of quadratic forms allows one to exclude infinitely many values of $n$.

Keywords: tight $t$-design, quadratic form.

Received: 01.11.2011

English version:
St. Petersburg Mathematical Journal, 2013, Volume 24, Issue 3, Pages 485–491
DOI: https://doi.org/10.1090/S1061-0022-2013-01249-0

Bibliographic databases:

Document Type: Article

Language: English

Citation: G. Nebe, B. Venkov, “On tight spherical designs”, Algebra i Analiz, 24:3 (2012), 163–171; St. Petersburg Math. J., 24:3 (2013), 485–491

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https://www.mathnet.ru/eng/aa1287

https://www.mathnet.ru/eng/aa/v24/i3/p163

This publication is cited in the following 14 articles:

Yuchen Xiao, Xiaosheng Zhuang, “Spherical Framelets from Spherical Designs”, SIAM J. Imaging Sci., 16:4 (2023), 2072
de Laat D. Machado F.C. de Oliveira Filho F.M. Vallentin F., “K-Point Semidefinite Programming Bounds For Equiangular Lines”, Math. Program., 194:1-2 (2022), 533–567
Peter Boyvalenkov, Hiroshi Nozaki, Navid Safaei, “Rationality of the inner products of spherical s-distance t-designs for t ≥ 2s - 2, s ≥ 3”, Linear Algebra and its Applications, 646 (2022), 107
Iverson J.W. King E.J. Mixon D.G., “A Note on Tight Projective 2-Designs”, J. Comb Des., 29:12 (2021), 809–832
Bannai E. Bannai E. Xiang Z. Yu W.-H. Zhu Ya., “Classification of Spherical 2-Distance (4,2,1)-Designs By Solving Diophantine Equations”, Taiwan. J. Math., 25:1 (2021), 1–22
Boyvalenkov P. Stoyanova M., “Linear Programming Bounds For Covering Radius of Spherical Designs”, Results Math., 76:2 (2021), 95
Peter Boyvalenkov, Navid Safaei, 2021 XVII International Symposium “Problems of Redundancy in Information and Control Systems” (REDUNDANCY), 2021, 101
A. Glazyrin, W.-H. Yu, “Upper bounds for $s$-distance sets and equiangular lines”, Adv. Math., 330 (2018), 810–833
E. Bannai, D. Zhao, L. Zhu, Ya. Zhu, Y. Zhu, “Half of an antipodal spherical design”, Arch. Math., 110:5 (2018), 459–466
H. Nozaki, Sh. Suda, “Complex spherical codes with three inner products”, Discret. Comput. Geom., 60:2 (2018), 294–317
E. Bannai, E. Bannai, H. Tanaka, Ya. Zhu, “Design theory from the viewpoint of algebraic combinatorics”, Graphs Comb., 33:1 (2017), 1–41
A. A. Makhnev, D. V. Paduchikh, M. M. Khamgokova, “Automorphisms of strongly regular graphs with parameters $(1305,440,115,165)$”, Proc. Steklov Inst. Math. (Suppl.), 304:1 (2019), S112–S122
D. G. Mixon, “Unit norm tight frames in finite-dimensional spaces”, Finite Frame Theory: a Complete Introduction To Overcompleteness, Proceedings of Symposia in Applied Mathematics, 73, ed. K. Okoudjou, Amer. Math. Soc., 2016, 53–78
Proc. Steklov Inst. Math., 288 (2015), 189–202

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	54
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