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Adding local short description: "Check digit algorithm", overriding Wikidata description "check digit algorithm presented by H. Michael Damm" |
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== Example ==
The following operation table will be used.<ref name="fenwick2014" /> It may be obtained from the totally anti-symmetric quasigroup {{math|''x'' ∗ ''y''}} in Damm's doctoral dissertation page 111<ref name="dhmd" /> by rearranging the rows and changing the entries with the permutation {{math|1=''φ'' = (1 2 9 5 4 8 6 7 3)}} and defining {{math|1=''x'' ⋅ ''y'' = ''φ''<sup>−1</sup>(''φ''(''x'') ∗ ''y'')}}.
{| class="skin-invert wikitable" style="text-align:center
|- style="color:#00A000"
|style="width:1.5em"| {{math|1=⋅}}
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=== Calculating the check digit ===
{| class="skin-invert wikitable" style="text-align:center
|- style="color:#00A000"
!style="color:black"| <span style="color:#00A000">digit to be processed</span> → column index
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=== Validating a number against the included check digit ===
{| class="skin-invert wikitable" style="text-align:center
|- style="color:#00A000"
!style="color:black"| <span style="color:#00A000">digit to be processed</span> → column index
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|style="width:1.5em"| 7
|style="width:1.5em"| 2
|style="width:1.5em"| 4
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| 9
| 7
| 4
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| 7
| 4
| '''0'''
|}
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