We give an explicit construction, based on Hadamard matrices, for an infinite
series of floor{sqrt{d}/2}-neighborly centrally symmetric d-dimensional
polytopes with 4d vertices. This appears to be the best explicit version yet of
a recent probabilistic result due to Linial and Novik, who proved the existence
of such polytopes with a neighborliness of d/400.Comment: 9 pages, no figure
