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We prove that a circulant Hadamard code of length $4n$ can always be seen asan HFP-code (Hadamard full propelinear code) of type $C_{4n}\times C_2$, where$C_2=\langle u\rangle$ or the same, as a cocyclic Hadamard code. We compute therank and dimension of the kernel of these kind of codes.

Circulant Hadamard matrices as HFP-codes of type $C_{4n}\times C_2$