ATRACTOR

Let us look at the main types of errors that this system detects. Firstly, it detects any singular error (that is, an error in a single digit). For example, ATM machines do not accept money transfers to an account whose NIB differs only in a single digit from a NIB of a real account (those NIB numbers simply do not exist in the system). And if we interchange two digits of the NIB, another common error? Neither. Since the transposition errors in the positions \(i\) and \(j\) are always detected when \(\mbox{mdc}\left(p_{i}-p_{j},\, k\right)=1\) (see details here) and, in the NIB code, since all weights are smaller than \(k=97\) and the latter is a prime number, that property holds (which means that any two-digit transposition changes always the check digits). Since these two types of errors are the most common, we may conclude that this is a good error-detecting code.

As you see, it is very unlikely that we will get money in our accounts from the mistakes of others ...

To check the detection rate of these two types of errors (or simply if you want to know if your NIB is correct) click here.

To know more about error detection in these identification systems, click here.

Beyond this example, check digits are used in many other systems like, for instance, Identity Cards, barcodes, banknotes, Visa Cards, ...