Below you find a few examples of codes that are used
to secure information.
A trivial way to secure your information is to keep copies of it.
A somewhat more advanced way is to include control characters
in your information. Suppose your information is a string
of zero's and one's, then you may add at each 8-th position a control
character equal to 0 or 1
such that the sum of the control character and the seven preceding ones
are even. So,
110110011010001110011
is transformed into
110110001101000111100111.
A mistake can be detected, but not corrected.
ISBN is the international standard book number.
It is a code that each officially
published book obtains.
This code consists of 9 digits followed by a 10-th symbol
from {0,1, ..., 9,
x}. The first 9 digits give information on
the book, like the year and place it is published.
The last symbol is a check symbol.
If the ISBN of a book is
a1a2 ···
a9b,
then the following relation is satisfied.
a1 + 2a2
···
+ 9a9 = b (mod 11)
Here 10 is represented by the symbol x.
If there is a mistake of +1 or -1 in the n-th symbol
of a1a2 ···
a9b, then
a1 + 2a2
···
+ 9a9 + 10b (mod 11)
equals +n or -n, respectively.
This makes it possible to detect and correct an error.