Some general notes related to your question:
- If the input is encoded as a vector of integers, then multiplication and addition are easy but bit shifting is hard. In this case, in BFV it typically requires bootstrapping (very expensive operation).
- If the input is in bits (for example, each coefficient represents a bit), then bit shifting is is not too hard (requires rotations in the worst case), but multiplication is hard (number of bits doubles with each multiplication).
In other words, evaluating the decryption circuit with BFV will be computationally expensive. This is why the community has focused on special ciphers, like PASTA, RASTA, and FASTA (see the other thread for details and references). These ciphers have an FHE-friendly decryption circuit. Using any LWC without considering the complexity of the decryption circuit from the FHE perspective may not be the best approach.