Tight t-designs and squarefree integers
European Journal of Combinatorics
On self-dual doubly-even extremal codes
Discrete Mathematics - Coding Theory
Coding theory and design theory: part II, design theory
Bounds for the number of nodes in Chebyshev type quadrature formulas
Journal of Approximation Theory
Construction of designs on the 2-sphere
European Journal of Combinatorics
Discrete Mathematics - A collection of contributions in honour of Jack van Lint
On the rigidity of spherical t-designs that are orbits of finite reflection groups
Designs, Codes and Cryptography
Codes and Siegel modular forms
Discrete Mathematics
Journal of Combinatorial Theory Series A
A Family of Optimal Packings in Grassmannian Manifolds
Journal of Algebraic Combinatorics: An International Journal
On designs in compact metric spaces and a universal bound on their size
Proceedings of the conference on Discrete metric spaces
Necessary conditions for existence of some designs in polynomial metric spaces
European Journal of Combinatorics
A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
Journal of Algebraic Combinatorics: An International Journal
Spherical 7-Designs in 2^n-Dimensional Euclidean Space
Journal of Algebraic Combinatorics: An International Journal
Overlap and Covering Polynomials with Applications to Designs and Self-Dual Codes
SIAM Journal on Discrete Mathematics
Designs in Grassmannian Spaces and Lattices
Journal of Algebraic Combinatorics: An International Journal
On Harmonic Weight Enumerators of Binary Codes
Designs, Codes and Cryptography
Association Schemes Related to Kasami Codes and KerdockSets
Designs, Codes and Cryptography
Improvement of the Delsarte Bound for &tgr;-Designs When It Is Not the Best Bound Possible
Designs, Codes and Cryptography
Asymmetric Cubature Formulae with Few Points in High Dimension for Symmetric Measures
SIAM Journal on Numerical Analysis
Spherical designs and finite group representations (some results of E. Bannai)
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
A Note on the Tight Spherical 7-Design in$${\mathbb R}^{23}$$ and 5-Design in$${\mathbb R}^{7*}$$
Designs, Codes and Cryptography
Journal of Algebraic Combinatorics: An International Journal
Matrix Groups Related to the Quaternion Group and Spherical Orbit Codes
Designs, Codes and Cryptography
Numerical Cubature Using Error-Correcting Codes
SIAM Journal on Numerical Analysis
Numerical Cubature from Archimedes' Hat-box Theorem
SIAM Journal on Numerical Analysis
A note on the spherical embeddings of strongly regular graphs
European Journal of Combinatorics
On antipodal Euclidean tight (2e + 1)-designs
Journal of Algebraic Combinatorics: An International Journal
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics)
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics)
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Existence of Solutions to Systems of Underdetermined Equations and Spherical Designs
SIAM Journal on Numerical Analysis
Orbits of the hyperoctahedral group as Euclidean designs
Journal of Algebraic Combinatorics: An International Journal
Imprimitive cometric association schemes: Constructions and analysis
Journal of Algebraic Combinatorics: An International Journal
On the strong non-rigidity of certain tight Euclidean designs
European Journal of Combinatorics
Improved Delsarte bounds for spherical codes in small dimensions
Journal of Combinatorial Theory Series A
Uniqueness of certain association schemes
European Journal of Combinatorics
On the rigidity of spherical t-designs that are orbits of reflection groups E8 and H4
European Journal of Combinatorics
Few-cosine spherical codes and Barnes--Wall lattices
Journal of Combinatorial Theory Series A
Note: Optimality and uniqueness of the (4,10,1/6) spherical code
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
European Journal of Combinatorics
New examples of Euclidean tight 4-designs
European Journal of Combinatorics
European Journal of Combinatorics
New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra
European Journal of Combinatorics
Note: Spherical two-distance sets
Journal of Combinatorial Theory Series A
Cubature formulas in numerical analysis and Euclidean tight designs
European Journal of Combinatorics
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
Association schemes and coding theory
IEEE Transactions on Information Theory
New code upper bounds from the Terwilliger algebra and semidefinite programming
IEEE Transactions on Information Theory
Linear programming bounds for codes in grassmannian spaces
IEEE Transactions on Information Theory
Commutative association schemes
European Journal of Combinatorics
Permutation group approach to association schemes
European Journal of Combinatorics
Some remarks on Euclidean tight designs
Journal of Combinatorial Theory Series A
Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes
European Journal of Combinatorics
Exact point-distributions over the complex sphere
Designs, Codes and Cryptography
Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere
SIAM Journal on Numerical Analysis
Journal of Algebraic Combinatorics: An International Journal
Cubic harmonics and Bernoulli numbers
Journal of Combinatorial Theory Series A
An excess theorem for spherical 2-designs
Designs, Codes and Cryptography
A unified approach to scattered data approximation on $\mathbb{S}^{\bf 3}$ and SO(3)
Advances in Computational Mathematics
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This survey is mainly intended for non-specialists, though we try to include many recent developments that may interest the experts as well. We want to study ''good'' finite subsets of the unit sphere. To consider ''what is good'' is a part of our problem. We start with the definition of spherical t-designs on S^n^-^1 in R^n. After discussing some important examples, we focus on tight spherical t-designs on S^n^-^1. Tight t-designs have good combinatorial properties, but they rarely exist. So, we are interested in the finite subsets on S^n^-^1, which have properties similar to tight t-designs from the various viewpoints of algebraic combinatorics. For example, rigid t-designs, universally optimal t-codes (configurations), as well as finite sets which admit the structure of an association scheme, are among them. We will discuss various results on the existence and the non-existence of special spherical t-designs, as well as general spherical t-designs, and their constructions. We will discuss the relations between spherical t-designs and many other branches of mathematics. For example: by considering the spherical designs which are orbits of a finite group in the real orthogonal group O(n), we get many connections with group theory; by considering those which are shells of Euclidean lattices, we get many unexpected connections with number theory, such as modular forms and Lehmer's conjecture about the zeros of the Ramanujan @t function. Spherical t-designs and Euclidean t-designs are special cases of cubature formulas in approximation theory, and thus we get many connections with analysis and statistics, and in particular with orthogonal polynomials, and moment problems. Moreover, Delsarte's linear programming method and many recent generalizations, including the work of Musin and the subsequent progress in using semi-definite programming, have strong connections with geometry (in particular sphere packing problems) and the theory of optimizations. These various connections explain the reason of the charm of algebraic combinatorics on spheres. At the same time, these theories of spherical t-designs and related topics have strong roots in the developments of algebraic combinatorics in general, which was started as Delsarte theory of codes and designs in the framework of association schemes.