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Definition. An $m\times n$ matrix is said to be a partial Hadamard matrix (let's say PHM) if its entries are chosen from $\lbrace -1, 1 \rbrace$ such that the dot product of each pair of row vectors ...

Assume the following matrix $$ E:=\left( \begin{array}{ccccc} e_1 & e_2 & \cdots & e_{p-1} & e_{p}\\ e_{p+1} & e_{p+2} & \cdots & e_{2p-1} & e_{2p} \\ \...

A pretty well-known theorem regarding linear $(n,k,d)$ codes is that every $n-d+1$ coordinate positions contain an information set, but not all $n-d$ coordinate positions do. This is equivalent to a ...