Yes, Raptor Codes are the specific ones used by NASA on their newest deep space missions link. Raptor codes are a type of fountain code.
Fountain codes are worth looking at if you haven't been keeping up with the latest and greatest Comp Sci developments in the last 15 years. With fountain codes you can break up a chunk of data into any number of unique packets. Any subset of those packets that add up to the size of the original packet can be used to reform the original file.
So say i had a 1MB file to send to Mars. I run a fountain encoder on that and i tell the encoder to make me 10,000,000 packets 1KB in size out of that 1MB file. So the fountain coder gives me 10GB of generated packets from that 1MB file. Now i spam those 10,000,000 packets across a really noisy connection. As soon as the receiver successfully receives any 1,001 of those packets (totalling up to just over 1MB worth of received packets) it can rebuild that file. I don't need to wait for retransmission requests or anything and it doesn't matter what packets make it or not. Just as long as the receiver can eventually successfully receive slightly over X bytes of data it can rebuild an X byte file.
Traditional error correction codes are great for correcting bit errors in a message that mostly gets there. Fountain codes on the other hand are great in situations where entire chunks of the desired message can be lost, they can avoid the retransmission of these lost packets entirely. The only issue is that they require redundancy in transmission in the first place.
It seems here they are grouping 50 packets of data together into 1 lot and making 50+R coded packets out of it where R is some number that's variable depending on how much loss they see. So they might send 60 coded packets. If any 50 of the 60 coded packets make it there they should have enough to rebuild the original 50 packets using fountain codes.