The number of a 5 Euro banknote starts with a land code of two letters, followed

Question

The number of a 5 Euro banknote starts with a land code of two letters, followed by 10 digits. For example, the land code UE stands for France. If we replace the letters of the alphabet by their two-digit positions in the alphabet (e.g. UE is replaced by 21 05), we find a number of in total 14 digits. It appears that the obtained number always equals 7 (mod 9). Is this code 1-error correcting? If so, why? If not, give an example of a number of a bank note that has one error in it that cannot be corrected.

Explanation / Answer

Q1)  Is this code 1-error correcting? - No this is not 1 error correcting because we have 2 errors in the Euro Note being modified, ie. UE (2 characters) are now replaced by 21 and 05 respectively. So U and E both these are modified and not just one. So this clearly isnt 1 error corrrecting.

Q2) If not, give an example of a number of a bank note that has one error in it that cannot be corrected.

If we have a note as EUXXXXXXXXXX, where X represents the digits, this contains an error that is EU doesnt represent any land code, but UE does (ie France). So in this example EUXXXXXXXXXX, it follows the pattern (starts with a land code of two letters, followed by 10 digits) but we cannot identify this error as the two letters are present. Now whether two letters are correct or not is something that cannot be detected. Hence, this is an example of a number of a bank note that has one error in it that cannot be corrected.

Please let me know in case of any clarifications required. Thanks!

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