Abstract. 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 R n 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.