I'm puzzled by the third para from the end about codon redundancy and how "it allows for the correction of errors", especially the sentence "If however the codons for all the other amino acids differ in at least two letters from the scrambled-up triple, the it's easy to guess that an error has been made and to deduce which amino acid was really meant".
Some concrete examples may help. Let's say the triplet GCU, which codes for alanine, is misread by one letter as GAU, which codes for aspartic acid. How do you get back from GAU to GCU? There are, and must be, other amino acids which differ only by one letter from GAU, for example GAA (glutamic acid), GGU (glycine). But even in those cases which differ by two from GAU, such as CGU (arginine), how is that relevant?
The most relevant passage from the companion article by Professor Budd, www.plus.maths.org/content/error-correcting-codes , seems to be the one about Hamming distances, but I just can't see how this applies here since there seems to be no question of adding extra parity digits.