Is maximizing hamming distance the same as minimizing correlation?
Two codewords $c_1$ and $c_2$ of length $n$, with elements in $\lbrace +1, -1 \rbrace$, and Hamming distance $d$, have a cross-correlation given by $$(n-d) -d = n-2d.$$ The reason is that there are $n-d$ bits that are equal and their product is $1$, and $d$ bits that are different and their product is $-1$.

Note that:


The larger the distance $d$, the smaller the correlation.
The correlation by itself does not tell you anything about the distance, since you also need to know $n$. For example, $1,1,1$ and $-1,-1,-1$ have correlation $-3$ but $1,1,1,1,1,1$ and $1,1,1,-1,-1,-1$ have correlation $0$.