Function to generate longer bit-sequence from shorter sequence with certain properties
Let $\pi$ be a random permutation on $\{1,\ldots,1024\}$, and let $K$ be a random bit string of length 1024 bits. The following mapping seems to satisfy your needs (with probability close to 1):
$$
A \mapsto \pi(A^{32} \oplus K).
$$
In particular, changing $b$ bits of $A$ will result in changing $32b$ bits of the result.

If you are OK with changing more than 32 bits, then you can take a random sparse affine function, that is the function whose $i$th bit is an XOR of a small number of bits of $A$ chosen at random, XORed with a random bit.