A family of small complete caps in PG(n,2)

The smallest known complete caps in PG(n,2) have size 23(2(n−6)/2)−3 if n≥10 is even and size 15(2(n−5)/2)−3 if n≥9 is odd. Here we give a simple construction of complete caps in PG(n,2) of size 24(2(n−6)/2)−3 if n is even and size 16(2(n−5)/2)−3 if n is odd. Thus these caps are only slightly larger than the smallest complete caps known in PG(n,2).