For the design of an error correcting code, I might wish to maximize the distance between the codewords $\sum a_i \oplus b_i$.
For spreading sequences I'd like to minimize the cross-correlation at $t=0$ of $\sum \sigma(a_i)\sigma(b_i)$ where $\sigma(\cdot)$ maps binary $0\to1$ and $1 \to (-1)$ (i.e. what you'd get out of a BPSK matched filter when $E_b$ is normalized and there is no noise).
Are these criteria the same? It seems to me that since $\sigma$ acts as an isomorphism that turns cyclic$\pmod 2$ addition into cyclic complex multiplication, they are equivalent statements. Can you verify this and let me know where I can read more about it?