geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are stud ...

, a spherical code with parameters (''n'',''N'',''t'') is a set of ''N'' points on the unit

hypersphere In mathematics, an -sphere or a hypersphere is a topological space that is homeomorphic to a ''standard'' -''sphere'', which is the set of points in -dimensional Euclidean space that are situated at a constant distance from a fixed point, cal ...

in ''n'' dimensions for which the

dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebra ...

of unit vectors from the origin to any two points is less than or equal to ''t''. The

kissing number problem In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement of ...

may be stated as the problem of finding the maximal ''N'' for a given ''n'' for which a spherical code with parameters (''n'',''N'',1/2) exists. The

Tammes problem In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the n ...

may be stated as the problem of finding a spherical code with minimal ''t'' for given ''n'' and ''N''.

External links

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A library of putatively optimal spherical codes
Coding theory {{Geometry-stub