There's a great chapter in "Group Theory in the Bedroom" [https://books.google.com/books/about/Group_Theory_in_the_Bed...] about the hunt for the mapping from DNA sequences to amino acids before the invention of X-ray crystallography allowed for direct observation of the machinery. Many elegant 3-letter mappings were hypothesized and tested chemically and statistically; they were all found to be incorrect.

Spoiler alert: once X-ray crystallography allowed for direct observation, the mapping was found to be a chaotic hodgepodge: some amino acids are coded by only one or two DNA triplets, and some are encoded by several. The only interesting property of the actual coding the book mentioned: the language is such that single-base errors in the triplet for an amino acid tended to result in a triplet that encoded to the same amino acid... For the amino acids involved in the most common cellular processes. In other words, transcription errors tend to not mess up the machinery in ways that are instantly fatal to the cell (because of course!).