Dense sphere packings from new codes (Q1575096)

The coset code construction allows to reduce the construction of sphere packings to error-correcting codes in a unified way. The authors have so constructed a large number of new binary, ternary, and quaternary linear error-correcting codes; in some dimensions this leads to improvements. They also express a recent construction of Vardy, that yielded record densities in 20, 27, 28, 29, and 30 dimensions, in the language of coset codes. Applying this method to dimension 18, they produce a sphere packing with record density \((3/4)^9\).