Can you elaborate on those coding problem reducible to homomorphic calculations? I'm very interested. I thought I heard the converse, homomorphic calculations using coding (my rough understanding of Learning With Errors).
Just to be clear, you're referring to coding theory (https://en.wikipedia.org/wiki/Coding_theory) in the sense of geometric codes from information theory, right? I fail to see an obvious way search engines fit in.
Search engines are the most common example, in general.