Abstract

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) .

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