Spherical codes and designs

From MaRDI portal

Publication:1245838

Jump to:navigation, search

DOI10.1007/BF03187604zbMath0376.05015OpenAlexW2584020404MaRDI QIDQ1245838

Philippe Delsarte, J. J. Seidel, Jean-Marie Goethals

Publication date: 1977

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03187604

Mathematics Subject Classification ID

Other designs, configurations (05B30) Metric geometry (51F99) Combinatorial aspects of finite geometries (05B25)

Related Items

Anticoherent subspaces, Construction of spherical cubature formulas using lattices, New Bounds for Spherical Two-Distance Sets, ON THE BOUNDEDNESS OF AN ITERATION INVOLVING POINTS ON THE HYPERSPHERE, The nonexistence of certain tight spherical designs, Tight relative t-designs on two shells in hypercubes, and Hahn and Hermite polynomials, Improvement of the Inside-Outside Duality Method, SPHERICAL DESIGNS FROM THE NORM-3 SHELL OF INTEGRAL LATTICES, Distance Sets on Circles, Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere, A recursive Lovász theta number for simplex-avoiding sets, New Bounds for Equiangular Lines and Spherical Two-Distance Sets, Bounds for sets with few distances distinct modulo a prime ideal, Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound, Delsarte’s extremal problem and packing on locally compact Abelian groups, Least distortion Euclidean embeddings of flat tori, t-Design Curves and Mobile Sampling on the Sphere, Spherical designs and modular forms of the \(D_4\) lattice, On the minimax spherical designs, Quadrature Rules for the Surface Integral of the Unit Sphere Based on Extremal Fundamental Systems, Absolute minima of potentials of certain regular spherical configurations, Optimal and extremal graphical designs on regular graphs associated with classical parameters, Doubly transitive lines. II: Almost simple symmetries, The spherical ensemble and quasi-Monte-Carlo designs, Odd strength spherical designs attaining the Fazekas-Levenshtein bound for covering and universal minima of potentials, Spherical Framelets from Spherical Designs, Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere, On the multiplicities of digraph eigenvalues, Euclidean designs obtained from spherical embedding of coherent configurations, Sketching with Spherical Designs for Noisy Data Fitting on Spheres, Is hyperinterpolation efficient in the approximation of singular and oscillatory functions?, The magic of 8 and 24, A UNIFORM PLACEMENT OF ALTERS ON SPHERICAL SURFACE (U-PASS) FOR EGO-CENTRIC NETWORKS WITH COMMUNITY STRUCTURE AND ALTER ATTRIBUTES, Unnamed Item, Estimates for Logarithmic and Riesz Energies of Spherical t-Designs, Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness, Efficient Spherical Designs with Good Geometric Properties, Weighted complex projective 2-designs from bases: Optimal state determination by orthogonal measurements, The simplest demonstrations of quantum nonlocality, Sidelnikov inequality and Legendre polynomials, On tight spherical designs, Mathematical aspects of molecular replacement. II. Geometry of motion spaces, Complex Spherical Designs and Codes, DIAGONAL-UNITARY 2-DESIGN AND THEIR IMPLEMENTATIONS BY QUANTUM CIRCUITS, New upper bounds for kissing numbers from semidefinite programming, On tight spherical designs, Point configurations that are asymmetric yet balanced, Unnamed Item, Definitions for spherical designs, Spherical Designs, Discrepancy and Numerical Integration, Estimates of the maximal value of angular code distance for 24 and 25 points on the unit sphere in \(\mathbb{R}^4\), Isometric embeddings of finite-dimensional $\ell_p$-spaces over the quaternions, The densest lattice in twenty-four dimensions, Spherical Designs and Nonconvex Minimization for Recovery of Sparse Signals on the Sphere, Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry, Toy models for D. H. Lehmer's conjecture, New Upper Bounds for Equiangular Lines by Pillar Decomposition, Numerical integration on graphs: Where to sample and how to weigh, Harmonic index \(t\)-designs in the Hamming scheme for arbitrary \(q\), Harmonic index \(t\)-designs in the Hamming scheme for arbitrary \(q\), Algebro-geometric aspectsof the Christoffel-Darboux kernelsfor classical orthogonal polynomials, Moment methods in energy minimization: New bounds for Riesz minimal energy problems, Bounds on the Maximum Number of Vectors with given Scalar Products, Exact Semidefinite Programming Bounds for Packing Problems, Chebyshev-type cubature formulas for doubling weighted spheres, balls, and simplexes, Upper bounds for packings of spheres of several radii, Kissing number in non-Euclidean spaces of constant sectional curvature, Majorization and Minimal Energy on Spheres, Symmetric informationally complete positive-operator-valued measures: A new computer study, Low-Rank Matrix Estimation from Rank-One Projections by Unlifted Convex Optimization, Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere, Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere, Bounds for spherical codes: The Levenshtein framework lifted, Sidel′nikov inequality, New Constructions of Codebooks Nearly Meeting the Welch Bound, Lasso Hyperinterpolation Over General Regions, Small designs for path-connected spaces and path-connected homogeneous spaces, Rényi formulation of uncertainty relations for POVMs assigned to a quantum design, On the explicit constructions of certain unitaryt-designs, On construction of finite averaging sets for SL(2,C) via its Cartan decomposition, Anticoherent spin-2 states and spherical designs, A new approach to the construction of optimal designs, On the number of nodes in \(n\)-dimensional cubature formulae of degree 5 for integrals over the ball, Balancedly splittable Hadamard matrices, Isometric embeddings and geometric designs, The spherical design algorithm in the numerical simulation of biological tissues with statistical fibre-reinforcement, Extremal polynomials for obtaining bounds for spherical codes and designs, Upper bounds for \(s\)-distance sets and equiangular lines, Johan Jacob Seidel, Some constructions of spherical 5-designs, Equidistant families of sets, Computing distance distributions of spherical designs, Interlacing eigenvalues and graphs, Asymptotically optimal designs on compact algebraic manifolds, On lower bounds on the size of designs in compact symmetric spaces of rank 1, Distributing many points on a sphere, McLaren's improved snub cube and other new spherical designs in three dimensions, Multi-scale structural modeling of soft tissues mechanics and mechanobiology, A new Euclidean tight 6-design, Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy, Ranks of matrices with few distinct entries, On the number of lattice points in a small sphere and a recursive lattice decoding algorithm, Distances, graphs and designs, On the connectivity of graphs in association schemes, Grassmannian frames with applications to coding and communication, Equiangular lines and spherical codes in Euclidean space, Strongly regular graphs having strongly regular subconstituents, Energy functionals, numerical integration and asymptotic equidistribution on the sphere., Lower bound for the number of nodes of cubature formulae on the unit ball, 6-transitive graphs, Harmonic index designs in binary Hamming schemes, New sets with large Borsuk numbers, Nonexistence of certain pseudogeometric graphs, On some spherical t-designs, On the weight distribution of spherical t-designs, Inhomogeneous extreme forms, Coherent configurations and triply regular association schemes obtained from spherical designs, Spherical 7-designs in \(2^n\)-dimensional Euclidean space, An upper bound for the cardinality of an s-distance subset in real euclidean space, Every large set of equidistant (0,+1,-1)-vectors forms a sunflower, Comparison of probabilistic and deterministic point sets on the sphere, Codes and designs in Grassmannian spaces., Spherical designs and finite group representations (some results of E. Bannai)., Spherical 5-designs obtained from finite unitary groups., On spherical codes with inner products in a prescribed interval, Construction of designs on the 2-sphere, The covering radius of spherical designs, Construction of spherical 4- and 5-designs, Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems, Polynomial approximation and quadrature on geographic rectangles, Bounds for the number of nodes in Chebyshev type quadrature formulas, Spherical 2-designs and lattices from abelian groups, Codes, cubes, and graphical designs, On maximal antipodal spherical codes with few distances, Universal lower bounds on energy and LP-extremal polynomials for \((4, 24)\)-codes, Optimal line packings from nonabelian groups, Universal optimal configurations for the \(p\)-frame potentials, Half of an antipodal spherical design, Complex spherical codes with three inner products, \(t\)-designs with general angle set, New spherical 4-designs, Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians, Designs as maximum codes in polynomial metric spaces, The cyclic edge-connectivity of strongly regular graphs, A geometrical characterization of strongly regular graphs, Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension, A criterion for a spherical design associated with V. A. Yudin potentials, Nonexistence of certain symmetric spherical codes, Galerkin approximation for elliptic PDEs on spheres, Deterministic constructions of compressed sensing matrices based on optimal codebooks and codes, A note on the tight spherical 7-design in \(\mathbb R^{23}\) and 5-design in \(\mathbb R^7\), Low dimensional strongly perfect lattices. IV: The dual strongly perfect lattices of dimension 16, Energy on spheres and discreteness of minimizing measures, On some recent progress in the classification of (\(P\) and \(Q\))-polynomial association schemes, Improve concentration of frequency and time (ConceFT) by novel complex spherical designs, Linear programming bounds for covering radius of spherical designs, Two constructions of asymptotically optimal codebooks via the trace functions, A new proof of a generalization of Gerzon's bound, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, On upper bounds for code distance and covering radius of designs in polynomial metric spaces, An upper bound for the size of \(s\)-distance sets in real algebraic sets, Bounds on antipodal spherical designs with few angles, Antipodal sets and designs on unitary groups, Polynomial spaces, Bounds on the measurable chromatic number of \({\mathbb{R}}\), Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics, On the spectrum of Markov operators of spherical designs, A construction of spherical 3-designs, On spherical t-designs in \(R^ 2\)., On designs in compact metric spaces and a universal bound on their size, A minimal design of order 11 on the 3-sphere, Numerical computation of triangular complex spherical designs with small mesh ratio, Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces, On the quadrature exactness in hyperinterpolation, Semi-device-independent quantum key agreement protocol, The minimal number of nodes in Chebyshev type quadrature formulas, Designs in Grassmannian spaces and lattices, Symmetric functions and spherical \(t\)-designs in \(\mathbb{R}^2\), Zonal functions for the unitary groups and applications to Hermitian lattices., On the rigidity of spherical \(t\)-designs that are orbits of finite reflection groups, Signed frames and Hadamard products of Gram matrices, On optimal tight 4-designs on 2 concentric spheres, Averaging sets: A generalization of mean values and spherical designs, Design-theoretic analogies between codes, lattices, and vertex operator algebras, A note on Assmus-Mattson type theorems, Polynomial properties on large symmetric association schemes, Some remarks on cubature formulas with linear operators, New spherical \((2 s + 1)\)-designs from Kuperberg's set: an experimental result, Extreme lattices and vexillar designs, Numerical verification methods for spherical \(t\)-designs, Some equalities and inequalities for probabilistic frames, Balanced sets and Q-polynomial association schemes, Finite groups admitting Grassmannian 4-designs, Sharp characters of finite groups, A copositive formulation for the stability number of infinite graphs, Bounding the diameter of distance. Regular graphs, Low rank matrix recovery from rank one measurements, On the tightest packing of sums of vectors, t-designs in projective spaces, A component-by-component approach to efficient numerical integration over products of spheres, Optimal asymptotic bounds for spherical designs, An extremum problem for polynomials and bounds for codes with given distance and diameter, Fisher type inequalities for Euclidean t-designs, Duality in coherent configurations, Tight 4 and 5-designs in projective spaces, Uncertainty principles for orthonormal sequences, On the existence of tight relative 2-designs on binary Hamming association schemes, A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness, Orbits of the hyperoctahedral group as Euclidean designs, Imprimitive cometric association schemes: constructions and analysis, Sphere packing bounds via spherical codes, Some remarks on Euclidean tight designs, Sparse grid quadrature on products of spheres, Spherical designs and heights of Euclidean lattices, The extendability of matchings in strongly regular graphs, Weighing matrices and spherical codes, Computational existence proofs for spherical \(t\)-designs, Linear programming bounds for regular graphs, Random tight frames, Cubic harmonics and Bernoulli numbers, On relative \(t\)-designs in polynomial association schemes, An excess theorem for spherical 2-designs, Invariants and Chebyshev polynomials, New parameters of subsets in polynomial association schemes, Numerical integration with polynomial exactness over a spherical cap, Some remarks on the Fejér problem for Lagrange interpolation in several variables, Bounds on three- and higher-distance sets, Minimization of the probabilistic \(p\)-frame potential, On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms, Tight 9-designs on two concentric spheres, Discrete spherical means of directional derivatives and Veronese maps, New asymptotic estimates for spherical designs, Rigidity of spherical codes, The Coulomb energy of spherical designs on \(S^{2}\), Hyperorthogonal family of vectors and the associated Gram matrix, Characterizations of regularity for certain \(Q\)-polynomial association schemes, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces, A survey on tight Euclidean \(t\)-designs and tight relative \(t\)-designs in certain association schemes, On the rigidity of spherical \(t\)-designs that are orbits of reflection groups \(E_8\) and \(H_4\), Complex spherical codes with two inner products, More constructions of near optimal codebooks associated with binary sequences, Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs, On spherical designs of some harmonic indices, A generalization of Larman-Rogers-Seidel's theorem, Cubature formulas in numerical analysis and Euclidean tight designs, Exact point-distributions over the complex sphere, Optimality and uniqueness of the Leech lattice among lattices, The Venkov inequality with weights and weighted spherical half-designs, A new asymptotic bound of the minimum possible odd cardinality of spherical \((2k-1)\)-designs, On a generalization of distance sets, Towards a proof of the 24-cell conjecture, On the equivalence between real mutually unbiased bases and a certain class of association schemes, Universal lower bounds for potential energy of spherical codes, A method for proving nonexistence of spherical designs of odd strength and odd cardinality, Optimality and uniqueness of the \((4,10,1/6)\) spherical code, Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets, Bounds for codes by semidefinite programming, Codebooks from almost difference sets, On tight projective designs, Polynomial techniques for investigation of spherical designs, Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps, New examples of Euclidean tight 4-designs, There are finitely many \(Q\)-polynomial association schemes with given first multiplicity at least three, On lattices whose minimal vectors form a 6-design, The \(s\)-energy of spherical designs on \(S^{2}\), On Weyl-Heisenberg orbits of equiangular lines, Tight t-designs and squarefree integers, Lower bounds for projective designs, cubature formulas and related isometric embeddings, Spherical two-distance sets, The Tietäväinen bound for spherical codes, A variational characterisation of spherical designs, Unitary designs and codes, A survey on spherical designs and algebraic combinatorics on spheres, Painless reconstruction from magnitudes of frame coefficients, A minimization problem for probabilistic frames, Lower bounds for measurable chromatic numbers, Regular two-distance sets, An addition formula for hyperbolic space, Parameters of t-designs in \({\mathbb{F}}P^{d-1}\), On tight t-designs in compact symmetric spaces of rank one, A construction of spherical 2-design, \(Q\)-polynomial coherent configurations, Few distance sets in \(\ell_p\) spaces and \(\ell_p\) product spaces, Design theory from the viewpoint of algebraic combinatorics, Rationality of the inner products of spherical \(s\)-distance \(t\)-designs for \(t \geq 2s - 2\), \(s \geq 3\), On the strong non-rigidity of certain tight Euclidean designs, Explicit spherical designs, Spherical $t_\epsilon $-designs for approximations on the sphere, Semidefinite programming bounds for the average kissing number, Geophysics and Stuart vortices on a sphere meet differential geometry, \(k\)-point semidefinite programming bounds for equiangular lines, On averaging sets, Octonions and the two strictly projective tight 5-designs, Improved Delsarte bounds for spherical codes in small dimensions, Tight Gaussian 4-designs, Minimization of energy per particle among Bravais lattices in ℝ²: Lennard–Jones and Thomas–Fermi cases, Designs, groups and lattices, Explicit construction of exact unitary designs, QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere, Modular forms and ellipsoidal \(T\)-designs, Optimal measures for \(p\)-frame energies on spheres, Discrepancy, separation and Riesz energy of finite point sets on the unit sphere, Distributed learning via filtered hyperinterpolation on manifolds, Classification of partially metric Q-polynomial association schemes with \(m_1=4\), Spherical 2-designs as stationary points of many-body systems, Remarks on Hilbert identities, isometric embeddings, and invariant cubature, The minimizers of the \(p\)-frame potential, High-dimensional sphere packing and the modular bootstrap, Frames over finite fields: basic theory and equiangular lines in unitary geometry, Generalized asymptotically optimal codebooks, Approximating the cone of copositive kernels to estimate the stability number of infinite graphs, Six constructions of asymptotically optimal codebooks via the character sums, Great antipodal sets on complex Grassmannian manifolds as designs with the smallest cardinalities, On the number of edges of a uniform hypergraph with a range of allowed intersections, Probabilistic tight frames and representation of positive operator-valued measures, Inside s-inner product sets and Euclidean designs, Maximal 2-distance sets containing the regular simplex, A short solution of the kissing number problem in dimension three, Bounds for the sum of distances of spherical sets of small size, Gaussian sums, hyper Eisenstein sums and Jacobi sums over a local ring and their applications, Nearly orthogonal vectors and small antipodal spherical codes, Upper bounds for energies of spherical codes of given cardinality and separation, Contact graphs of ball packings, Bounds on sets with few distances, Constructions and restrictions for balanced splittable Hadamard matrices, Low-energy points on the sphere and the real projective plane, On antipodal Euclidean tight \((2e+1)\)-designs, On polarization of spherical codes and designs, Pseudo-normalized Hecke eigenform and its application to extremal 2-modular lattices, Geometric aspects of 2-walk-regular graphs, Minimal weighted 4-designs on the sphere \(S^2\), Cayley sum graphs and their applications to codebooks, Quadrature formulas for Bessel polynomials, On tight 4-designs in Hamming association schemes, Upper energy bounds for spherical designs of relatively small cardinalities, Delaunay polytopes derived from the Leech lattice, Spherical \((t,t)\)-designs with a small number of vectors, Biangular lines revisited, Classification of spherical 2-distance \(\{4,2,1\}\)-designs by solving Diophantine equations, QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY, Doubly transitive lines. I: Higman pairs and roux, Asymptotically optimal cubature formulas on manifolds for prefixed weights, Conformal designs based on vertex operator algebras, Lattices of Simplex Type, Tight \(p\)-fusion frames, Harmonic singular integrals and steerable wavelets in \(L_2(\mathbb R^d)\), Well-separated spherical designs, Matrix groups related to the quaternion group and spherical orbit codes, On Euclidean tight 4-designs, On representations of graphs as two-distance sets, Equiangular lines and the Lemmens-Seidel conjecture, Bounds on Equiangular Lines and on Related Spherical Codes, Quadrature rules with neighborhood of spherical designs on the two-sphere, Remarks on the concepts of \(t\)-designs, Quadrature points via heat kernel repulsion, Invariant Semidefinite Programs, SHELLS OF SELFDUAL LATTICES VIEWED AS SPHERICAL DESIGNS, Numerical construction of spherical \(t\)-designs by Barzilai-Borwein method, On spherical designs obtained from Q-polynomial association schemes, Extremal properties of spherical semidesigns, Spherical half-designs of high order, Graphs and spherical two-distance sets, Two constructions of asymptotically optimal codebooks, Rational designs, Construction ofk-Angle Tight Frames, Energy bounds for codes in polynomial metric spaces, Lattices from tight frames and vertex transitive graphs, An Approach to the Dodecahedral Conjecture Based on Bounds for Spherical Codes, Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations, Universally optimal distribution of points on spheres, ASYMPTOTIC LINEAR PROGRAMMING LOWER BOUNDS FOR THE ENERGY OF MINIMIZING RIESZ AND GAUSS CONFIGURATIONS, On Euclidean designs, Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments, Spherical designs of harmonic index \(t\), On the ideal of the shortest vectors in the Leech lattice and other lattices, Finite two-distance tight frames, Perfect state transfer on distance-regular graphs and association schemes, Distributing many points on spheres: minimal energy and designs, Approximately strongly regular graphs, Disjoint weighing matrices, Complete positivity and distance-avoiding sets

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1245838&oldid=13332121"