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I am a hobby computer scientist and I have a problem to which I am searching an efficient algorithm. Given an integer n, we want to combine some square input-matrices of size n in a way that is ...

Assume that $n$ is a sufficiently large number. Is there a Hadamard matrix $H_{4n \times 4n}=(h_{ij})$ with the last row and the last cloumn $J$ (thet is, for every $k$, $h_{k,4n}=1$ and $h_{4n, k}=1$)...