New Upper Bounds on Sphere Packings I
نویسنده
چکیده
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
منابع مشابه
New Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
متن کاملNew Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
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We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
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Using lower bounds on distance spectrum components of a code on the Euclidean sphere, we improve the known asymptotical upper bounds on the cardinality of multiple packings of the sphere by balls of smaller radii. Let Rn be the n-dimensional Euclidean space, and Sn−1(r) ⊂ Rn be the (closed) Euclidean sphere of radius r with the center in the origin. Let further S̃n−1(r, ā) be the open ball of ra...
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