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Difference between revisions of "Sphere packing"

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Sphere  packing has various applications in error-correcting codes (cf.  [[Error-correcting code|Error-correcting code]]), the channel coding  problem, Steiner systems (cf. [[Steiner system|Steiner system]]), <img align="absmiddle" border="0"  src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071050/p07105021.png" />-designs, and in  the theory of finite groups. The most important special case is the sphere packing in <img align="absmiddle" border="0"  src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071050/p07105022.png" /> via the [[Leech  lattice|Leech lattice]]. Finite and infinite sphere packing in <img  align="absmiddle" border="0"  src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071050/p07105023.png" /> has applications  in classical and modern crystallography (cf. [[Crystallography,  mathematical|Crystallography, mathematical]]).
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Sphere  packing has various applications in [[error-correcting code]]s, the channel coding  problem, [[Steiner system]]s, $t$-designs, and in  the theory of finite groups. The most important special case is the sphere packing in $\R^{24}$ via the [[Leech  lattice]]. Finite and infinite sphere packing in $\R^3$ has applications  in classical and modern [[Crystallography,  mathematical|crystallography]].
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J.H. Conway,   N.J.A. Sloane,   "Sphere packing, lattices and groups" , Springer (1988)
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J.H. Conway, N.J.A. Sloane, "Sphere packing, lattices and groups" , Springer (1988)

Latest revision as of 01:32, 11 February 2012

Sphere packing has various applications in error-correcting codes, the channel coding problem, Steiner systems, $t$-designs, and in the theory of finite groups. The most important special case is the sphere packing in $\R^{24}$ via the Leech lattice. Finite and infinite sphere packing in $\R^3$ has applications in classical and modern crystallography.

J.H. Conway, N.J.A. Sloane, "Sphere packing, lattices and groups" , Springer (1988)

How to Cite This Entry:
Sphere packing. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sphere_packing&oldid=20966
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