What is the code for the rings stamped on the top of canned food?

There’s no hidden code in the rings, they are just there to stabilize the thin metal.

A flat sheet is weaker and more flexible than one with ridges - the same reason why roof and wall metal is usually corrugated. On taller cans you will often also find corrugated areas on the sides of the can, hidden by the paper label.

Actually, there can be encoded information stamped into the can ends, but it's probably not what you're thinking it is.

The presses which make the ends from sheets of metal usually contain multiple dies. Each time the press cycles, the dies stamp out an individual can end.

In some cases the individual dies are identified by a small mark in the pattern of beads (rings) and panels that are stamped into the ends. The pattern of beads and panels themselves don't mean anything, but the ID marks found in the beads can convey meaning. The pattern of ID marks varies from press to press, and manufacturer to manufacturer. Many ends don't even have these marks, but many do.

Here's a disappointingly poor picture from the Canadian government which almost shows the ID marks on a can end:

The first "bead" of the gold-colored end in the bottom right portion of the graphic shows a couple ID marks a the end of the arrow.

Here's another picture from the same source that shows an ID mark on a can end:

The ID mark is the one at roughly the 10-o'clock position. The "feature" at the 12-o'clock position is a defect.

For anyone who is interested, more information from the Canadian government regarding the inspection of food cans can be found here... (I used to be a food can inspector in a previous life and this is an excellent summary of can defects, their causes, and the manufacturing process in general. I encourage all "foodies" to check it out! Guaranteed to slow up your next visit to the grocery by at least 30 minutes....)

Apart from keeping track of the manufacturing processes, machine conditions, etc. there's no "code" which translates to the contents of the can or the filling operations.

The ID marks tell the people who run the end presses which die, and which machine, the end came off of. They can also identify which sets of dies are installed in the machine as that can vary depending on metal thickness, maintenance requirements, etc. and for keeping sets together appropriately and so on.

The same end presses are generally used to make a variety of can ends, for a variety of foods so any ends made on a particular press could end up on anything in the grocery.