January 2008
Intermediate to advanced
384 pages
8h 1m
English
Content preview from Joe Celko's Thinking in Sets: Auxiliary, Temporal, and Virtual Tables in SQLBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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8.3. Classes of Algorithms
The most common check digit procedures come in a few broad classes. One class takes the individual digits, multiplies them by a constant value (called a weight) for each position, sums the results, divides the sum by another constant, and uses the remainder as the check digit. These are called weighted-sum algorithms.
Another approach is to use functions based on group theory, a branch of abstract algebra; these are called algebraic algorithms. A discussion of group theory is a little too complex to take up here, so I will do a little hand-waving when I get to the mathematics. Finally, you can use lookup tables for check digit functions that cannot be easily calculated.
The lookup tables can be almost anything, including ...
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