Here are some Pros and Cons for each approach:

List

Pros

• No predictable pattern for users to exploit
• You don't need to generate an encoding/decoding

Cons

• Only represents pre-defined states
• Gets messy/large when storing many states

Binary representation

Pros

• Represent a wider variety of data/states (create a password for any given state of the game)

Cons

• Difficulty of implementation

If you are going to use binary representation, I suggest you use something like base16/base32/base64 values depending on your data size.