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The scheme, nevertheless, appears to work exactly because of the fixed initial 0.
The recent [https://en.wikipedia.org/w/index.php?title=Damm_algorithm&diff=prev&oldid=614858206 edit] added possible justification for this stating that for this modified equation only a weak totally anti-symmetric quasigroup with additional property of {{math|1=''x'' ∗ ''x'' = 0}} is needed. I can easily see that other statements (definition of weak totally anti-symmetric, and that existence of weak of given order implies existence of totally anti-symmetric and that one can be constructed from another with appropriate permutation) are present in the referenced dissertation (and they are restated later in English in ScienceDirect article, referenced as well), but I can't find anything about using fixed prefix. Did I miss something or are we missing some important references? — [[User:MwGamera|mwgamera]] ([[User talk:MwGamera|talk]]) 19:11, 29 June 2014 (UTC)
:The reference is:
:{{cite book |last=Fenwick |year=2014 |first=Peter |title=Introduction to Computer Data Representation |chapter=Checksums and Error Control |doi=10.2174/9781608058822114010013 |pages=[http://ebooks.benthamscience.com/sample/9781608058822/51/ 191–218] |publisher=Bentham Science Publishers |isbn=978-1-60805-883-9 }}
<blockquote>
Assuming a number … and a "working digit" w we then –
# Set w = 0
# Successively set w = M[w, d<sub>i</sub>], working from the left (row w, column d<sub>i</sub> of the matrix).
# Append the final w as the check digit.
</blockquote>
--[[User:W96|W96]] ([[User talk:W96|talk]]) 18:51, 18 January 2015 (UTC)
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