How to show if ISBN code can self-repair by Hamming distance?

Question

I found this filled college worksheet. It states that minimum (Hamming) distance of ISBN code is 2 (Excercise 5). I know how to prove this and why is that. But then in excercise 8 it states that ISBN cannot self-repair, if n-th digit is corrupted and n is not known.

To show why, it references Ex. 5 and place:

H(x,y) = 2 < 2(1) + 1.

How is this showing that ISBN cannot correct single digit in general? What kind of formula is this?

Answer 1

Ok. I probably already found an answer. If you want to add something, please feel free for any other people.

A code C is said to be k-errors correcting if, for every word w in the underlying Hamming space H, there exists at most one codeword c (from C) such that the Hamming distance between w and c is at most k. In other words, a code is k-errors correcting if, and only if, the minimum Hamming distance between any two of its codewords is at least 2k+1

Wikipedia from Robinson, Derek J. S. (2003). An Introduction to Abstract Algebra. Walter de Gruyter. pp. 255–257. ISBN 978-3-11-019816-4.