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- The first array contains the result of "Dihedral D5" multiplication;
- The second array consists of 8 rows of which two are defined while the rest are derived by applying the following formula: F(i, j) = F(i - 1, F(1, j)) ;
- The third array consists of a single row containing the inverse of the Dihedral D5 array it identifies the location of all the zero values in the first array.
| Caption label | ||||
|---|---|---|---|---|
| ||||
Results of Dihedral D5 multiplication |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
1 | 1 | 2 | 3 | 4 | 0 | 6 | 7 | 8 | 9 | 5 |
2 | 2 | 3 | 4 | 0 | 1 | 7 | 8 | 9 | 5 | 6 |
3 | 3 | 4 | 0 | 1 | 2 | 8 | 9 | 5 | 6 | 7 |
4 | 4 | 0 | 1 | 2 | 3 | 9 | 5 | 6 | 7 | 8 |
5 | 5 | 9 | 8 | 7 | 6 | 0 | 4 | 3 | 2 | 1 |
6 | 6 | 5 | 9 | 8 | 7 | 1 | 0 | 4 | 3 | 2 |
7 | 7 | 6 | 5 | 9 | 8 | 2 | 1 | 0 | 4 | 3 |
8 | 8 | 7 | 6 | 5 | 9 | 3 | 2 | 1 | 0 | 4 |
9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| Caption label | ||||
|---|---|---|---|---|
| ||||
The full array for Function F |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
1 | 1 | 5 | 7 | 6 | 2 | 8 | 3 | 0 | 9 | 4 |
2 | 5 | 8 | 0 | 3 | 7 | 9 | 6 | 1 | 4 | 2 |
3 | 8 | 9 | 1 | 6 | 0 | 4 | 3 | 5 | 2 | 7 |
4 | 9 | 4 | 5 | 3 | 1 | 2 | 6 | 8 | 7 | 0 |
5 | 4 | 2 | 8 | 6 | 5 | 7 | 3 | 9 | 0 | 1 |
6 | 2 | 7 | 9 | 3 | 8 | 0 | 6 | 4 | 1 | 5 |
7 | 7 | 0 | 4 | 6 | 9 | 1 | 3 | 2 | 5 | 8 |
| Caption label | ||||
|---|---|---|---|---|
| ||||
The Inverse D5 array |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|
|---|---|---|---|---|---|---|---|---|---|---|
0 | 4 | 3 | 2 | 1 | 5 | 6 | 7 | 8 | 9 |
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The identifier is checked by starting at the rightmost digit of the identifier (the check-digit itself) and proceeding to the left processing each digit as follows:
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