https://www.sciencedirect.com/science/article/abs/pii/S00225...
Now, I'm not an expert or even an advanced layperson in this area, so I won't attempt to speak to the validity of the idea. I merely found the argument interesting at the time.
First they propose a genetic code that is totally unrelated to the current one. It can be perfectly the table of a totally different lifeform. The transition they propose looks too difficult, almost impossible.
Probably we had a transition from RNA to DNA a loooong time ago, but they have a 1 to 1 translation, and the intermediate steps look useful. But no one is sure anyway.
They propose a change where almost all the table changes and almost all the internal structure of the table change.
It is very strange that they have 20 amino acids and no stop code. A proposal with 19 amino acids and a stop code looks more sensible. We know that it is possible to add new amino acids to the table (with enough time). I think the main problem is that using 19 amino acids and a stop code breaks the magical part of predicting the number 20 with pencil and paper.
To make the table work, you need the correct transfer-RNA. To get all the symmetries in their model you need to be really lucky. In the block model of 15+1 you any random selection of tRNA is fine if it ignore the last base.
Another big problem is that they predict that half of the proteins would have been constructed backward. But as they say this make proteins not fold correctly. They try to avoid the problem using palindromic proteins, that is not supported by evidence.
DNA and RNA: Perhaps they are inevitable, and any lifeforms have the same molecules and bases. Perhaps some lifeform can use only the methylated versions? Is ribose inevitable? Is 3 bases per codon inevitable? But I think there is a chance for inevitability.
The list of amino acids is somewhat random. We use 20, Some bacteria use a 1 or 2 more. And we can transform in place the amino acid inside a protein into another amino acid. I expect a similar list of 20+-5 amino acids. A perfect coincidence would be too hard, but it is not even true for terrestrial life.
The most interesting part is the Genetic Code https://en.wikipedia.org/wiki/Genetic_code that translate the 4^3=64 combinations of bases in the DNA to the 20 amino acids. As far as we know it is random. It has some internal structure, for example the code is mostly like 16 blocks to encode 15 amino acids and a stop signal, and a few tweaks here and there to break some block to encode the other 5 amino acids. But as far as we know there are no reasons to choose each block as us.
Some bacteria use versions with small tweaks, with one or two changes, so we know it if possible to change it, but very difficult to make a total rewrite.
If the life out there use the same Genetic Code (with a few tweaks) it is almost sure it is related to us.