Density Doubling, Double-circulants, and New Sphere Packings
نویسنده
چکیده
New nonlattice sphere packings in dimensions 20, 22, and 44–47 that are denser than the best previously known sphere packings were recently discovered. We extend these results, showing that the density of many sphere packings in dimensions just below a power of 2 can be doubled using orthogonal binary codes. This produces new dense sphere packings in Rn for n = 25, 26, . . . , 31 and 55, 56, . . . , 63. For n = 27, 28, 29, 30 the resulting packings are denser than any packing previously known.
منابع مشابه
Dense Sphere Packings from New Codes
The idea behind the coset code construction (see [G.D. Forney, Coset Codes, IEEE Transactions on Information Theory, Part I: Introduction and Geometrical Classification, pp. 1123–1151; Part II: Binary lattices and related codes, pp. 1152–1187; F.R. Kschischang and S. Pasupathy, IEEE Transactions on Information Theory 38 (1992), 227–246.]) is to reduce the construction of sphere packings to erro...
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