While that sounds really cool, if computing your convention is more complicated that consulting a giant lookup table, it would be reasonable to expect you to describe it that way.

There are 35 bids, (plus passing, doubling, and redoubling), which are ordered so you cannot make a bid that comes before that last one made, and the last bid made is important for the next phase of the game. You have less than 6 bits with every bid. You want your first bid to transmit info about your hand, not part of a key.

In the next phase, you play one of the cards in your hands in each trick, your hand starts with 13 cards and is not replenished, and you do not know when setting up your convention which cards you hold (the point is to communicate which cards you hold), there are restrictions on which cards you can play, and you also want to play the card that wins the trick (and preparing to win later tricks is why you would be communicating about your hand). You have less than 4 bits in this phase.