Haven't studied it, but you are going to need the whole story, coding structures, bandwidth, ECC methods, etc.

Coding theory and ECC is a field of math/engineering that can get a bit "too interesting" for some. I went that path for a while in the field of disk drives, the coding and ECC things there are pretty complex.

What you mention of the capability to "mess up" 6 other bits does not take into account the detection scheme and the weighting of each delay tap. I expect whats getting used is a Viterbi detector and some for of "partial response" with "maximum likelihood" detection...The contribution from a single bit is actually spread across several time windows and has to be properly weighted in (or out) of the adjacent windows.

Anyhow it becomes a communication channel problem with needs to look at the model end to end, Some things will be in the PHY levels but a lot is not.