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{{oldafdfull| date = 22 December 2012 (UTC) | result = '''keep''' | page = Damm algorithm }}{{WikiProject banner shell|class=Start}}
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* <nowiki>[[Exponentiation#In abstract algebra|powers]]</nowiki> The anchor (#In abstract algebra) has been [[Special:Diff/1042507126|deleted by other users]] before. <!-- {"title":"In abstract algebra","appear":{"revid":297269046,"parentid":297268883,"timestamp":"2009-06-19T00:29:27Z","removed_section_titles":["Generalizations of exponentiation","Exponentiation in abstract algebra","Exponentiation over sets","Exponentiation in category theory","Exponentiation of cardinal and ordinal numbers"],"added_section_titles":["Generalizations","In abstract algebra","Over sets","In category theory","Of cardinal and ordinal numbers"]},"disappear":{"revid":1042507126,"parentid":1042500891,"timestamp":"2021-09-05T10:01:01Z","removed_section_titles":["In abstract algebra"],"added_section_titles":[]}} -->
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: I am not quite sure what you mean with "rearranging the rows works" -- perhaps that the resulting quasigroup is still totally anti-symmetric? Well, I have not thought about your argument, but what I can say is that the table given on this Wikipedia page is not totally anti-symmetric, and hence the resulting checksum code does *not* detect all transposition errors. E.g. 41 and 14 both have checksum 1. While I am at it, I am confused as to why one would copy the quasigroup multiplication table from page 111 in Damm's thesis, which is inside a screenshot, instead of, say, taking the one on page 106... [[User:BlackFingolfin|BlackFingolfin]] ([[User talk:BlackFingolfin|talk]]) 08:49, 23 March 2015 (UTC)
:: After rearranging rows, the resulting quasigroup is ''weakly'' totally anti-symmetric. As you noticed 14 = 41, which violates the second requirement for TA-quasigroups. But notice that ''a''14 ≠ ''a''41 for all ''a'' ∈ ''Q'' and the algorithm described in the article uses a fixed prefix of ''a'' = 0 (interim digit initialized to 0), thus still detecting all adjacent transpositions. — [[User:MwGamera|mwgamera]] ([[User talk:MwGamera|talk]]) 16:18, 23 March 2015 (UTC)
::: You are of course completely right -- I stupidly overlooked the initial 0 in the algorithm and examples, ouch. Thanks for taking the time to set me straight :). [[User:BlackFingolfin|BlackFingolfin]] ([[User talk:BlackFingolfin|talk]]) 08:26, 24 March 2015 (UTC)
== Trailing zeros? ==
The article explains that leading zeros have no effect on the checksum but that is probably not a weakness but a strength. If there is a weakness, surely it is that trailing zeros have no effect? 13, 130, 1300 and 13000 are all valid. An easy defence would be to reject all numbers ending in (one or more) zeros. [[User:Johnhwoods|Johnhwoods]] ([[User talk:Johnhwoods|talk]]) 08:44, 14 April 2024 (UTC)
Whilst I'm thinking about zeros, the weaknesses section says that no checksum algorithm is affected by leading zeros. But it looks to me like Verhoeff is.
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