Spherical codes and designs

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August undefined, 2024

WebApr 4, 2024 · Keywords. Spherical codes and designs, s-distance sets MSC Codes. 05B30 1. Introduction Let Sn−1 be the unit sphere in Rn. A ﬁnite set C ⊂ Sn−1 is called a spherical …

(PDF) On polarization of spherical codes and designs

WebApr 11, 2024 · This paper presents the design and implementation of a spherical robot with an internal mechanism based on a pendulum. The design is based on significant improvements made, including an electronics upgrade, to a previous robot prototype developed in our laboratory. WebIntroduction Spherical designs and codes on complex unit sphere, by Roy and S. (2014) Journal of Combin. Des. with a connection to association schemes. Ω d): the unit sphere of Cd. For X ˆ Ω d), de ne A(X) := x;y j x;y 2 X;x ̸= yg. Remark.. Sd 1: the unit sphere of Rd) real spherical designs and codes. X ˆ Ω d) with absolute values of inner products) complex … daren williams almond board

On polarization of spherical codes and designs - ScienceDirect

WebMar 1, 2014 · Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high... WebAug 1, 1994 · Abstract We find the distance distributions (of a spherical code) with respect to every point for the tight spherical 4-, 5-, and 7-designs. As an immediate corollary we … WebMay 29, 2024 · Ericson and Zinoviev mentioned in the introduction that Spherical codes have many applications in physics or biology. Other papers support this claim. But at this … darent valley hospital scbu

An improved algorithm for proving nonexistence of small spherical designs

Spherical codes Henry Cohn

WebAug 1, 2009 · Spherical codes and spherical designs are nothing but finite subsets of Sn−1. Roughly speaking, the code theoretical viewpoint is to try to find X, whose points are … WebThe spherical code problem asks how to arrange N points on the surface of the unit sphere S n-1 in n dimensions so as to maximize the distance between the nearest pair of points. … darent valley willow wardWebDec 25, 2008 · [1] gives an optimal antipodal spherical (35, 240, 1/7) code whose vectors form a spherical 3-design. Generalizing the study [1], [5] gives a construction of spherical 3-designs. ...... dareof.aryland

"WebMar 1, 2014 · Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the … " - Spherical codes and designs

Spherical codes and designs

New York Journal of Mathematics - University at Albany, SUNY

WebJun 1, 2013 · Delsarte, Goethals and Seidel [14,Example 8.3] show that equality holds if and only if the union of the code with its antipodal code is a tight spherical 5-design, and in this case Cohn and Kumar ... WebJun 1, 1981 · Tables of sphere packings and spherical codes Authors: N. J. A. Sloane The OEIS Foundation Inc. Abstract The theta function of a sphere packing gives the number of centers at each distance from...

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WebJul 24, 2015 · Spherical Designs in Four Dimensions (Extended Abstract) Full-text available Article N. J. A. Sloane R. H. Hardin Philippe Cara View Show abstract ... In two dimensions (d = 1) the problem is... WebLet X ⊂ Rm be a spherical code (i.e., a finite subset of the unit sphere) and consider the ideal of all polynomials in m variables which vanish on X. Motivated by a study of cometric (Q …

http://www.neilsloane.com/ WebApr 25, 2011 · Complex spherical designs and codes. Aidan Roy, Sho Suda. Real spherical designs and real and complex projective designs have been shown by Delsarte, …

Seidel's selected papers are divided into four areas: graphs and designs; lines with … Via the theory of error-correcting codes, we construct here several new 5-designs on … The absolute bound for the cardinality of sets of lines in R n or C n having a … Tri-weight codes and generalized Hadamard matrices. Information and … Bemerkungen zur Theorie der beschrankten Bilinearformen mit unendlich vielen … WebT1 - Spherical codes and designs. AU - Delsarte, Ph. AU - Goethals, J.M. AU - Seidel, J.J. PY - 1977. Y1 - 1977. N2 - No abstract. AB - No abstract. U2 - 10.1007/BF03187604. DO …

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WebJul 15, 2024 · We derive universal lower and upper bounds on the polarization of spherical designs of fixed dimension, strength, and cardinality. The bounds are universal in the … darent valley trout fishersWebMoreover, we discuss the relation between equiangular lines and spherical two-distance sets and we obtain the new results on the maximum spherical two-distance sets in R n up to n ≤ 417. Keywords equiangular lines two-distance set semidefinite programming MSC codes Primary 52C35; Secondary 14N20 90C22 90C05 Get full access to this article daren wrideWebSpherical codes and designs SpringerLink Published: September 1977 Spherical codes and designs P. Delsarte, J. M. Goethals & J. J. Seidel Geometriae Dedicata 6 , 363–388 ( … dare nursing notesWebDec 1, 1995 · We prove that all spherical codes attaining the “even” Levenshtein bounds are tight spherical designs. Then we use the known classification results to describe such … darent valley maternity unitWebThe following tight spherical t -designs are unique: the 5-design in Ω 7, the 7-designs in Ω 8 and Ω 23, and the 11-design in Ω 24. It was shown in [20] that the maximum number of … birth rights maternityWebOct 8, 2024 · We investigate spherical 4-distance 7-designs by studying their distance distributions. We compute these distance distributions and use their product (an integer) to derive certain divisibility... darenth valley fishing lakesWebSpherical codes (packings) Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry) Spherical codes (coverings) Spherical codes (t-designs) Spherical codes (minimal potential energy arrangements) Spherical codes (maximal volume arrangements) Packings of lines, planes etc.: packings in Grassmannian … birth rights bar association