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Dense sphere packings from new codes

Journal of Algebraic Combinatorics, 11 (2000), 95-100.

doi:10.1023/A:1008733715001

Abstract:

The idea behind the coset code construction is to reduce the construction of sphere packings to error-correcting codes in a unified way. We give here a short self-contained description of this method. In recent papers we constructed a large number of new binary, ternary and quaternary linear error-correcting codes. We present a table with the largest densities of sphere packings known to us in dimensions up to 200. In many dimensions our new codes yield improvements. Recently Vardy has found a construction, which yields record densities in dimensions 20,27,28,29 and 30. We give a short description of his method using the language of coset codes. Moreover we are able to apply this method in dimension 18 as well, producing a sphere packing with a record center density of (3/4)⁹.

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