Intersection of Hadamard Codes

For two binary codes C₁,C₂, define i(C₁ ,C₂)=|C₁capC₂| to be their intersection number. This correspondence establishes that there exist Hadamard codes of length 2^t, for all tges3, with intersection number i if and only if iisin{0,2,4,...,2^t+1-12,2^t+1-8,2^t+1}. Also it is proved that for all tges4, if there exists a Hadamard matrix of order 4s, then there exist Hadamard codes of length 2^t+2 s with intersection number i if and only if iisin{0,2,4,...,2 ^t+3s-12,2^t+3s-8,2^t+3s}