Talk:Verhoeff algorithm

Is this algorithm correct?

According to [1], 3170092 is also a valid number.

Using the algorithm here, that becomes:

i	n_i	p(i,n_i)	previous c	new c = d(c,p(i,n_i))
0	2	2	0	2
1	9	4	2	1
2	0	5	1	6
3	0	8	6	3
4	7	8	3	6
5	1	2	6	9
6	3	3	9	6

Which one is incorrect? The wikiarticle? The other article? The fact that 3170092 is a valid number? Or have I made a mistake?

As best I can tell, the Marist College article you cited is wrong. The position-based permutation which Verhoeff settled on (the p table) is not a simple exponential of the group multiplication (the d table), as the article you found claims.

My understanding (from the first reference in the Wikipedia article) is that Verhoeff experimented with many different permutations before coming up with one that worked particularly well. A simple exponential permutation would actually be atrociously bad, since multiplication in the dihedral group contains two cycles of period 2 — namely, (14) and (23) — and one cycle of period 1 — namely, (0).

Richwales 20:50, 24 September 2006 (UTC)[reply]

195.224.169.69 19:29, 26 September 2006 (UTC) Thanks for the information.[reply]

I don't understand the following description:

"The involved nature of the Verhoeff check might especially be seen as a drawback if the client applications within a system need to explicitly identify ID's that fail the check digit test. If it is sufficient for a client to look up each ID in a master database and report malformed values as "not found," then only the piece of the system that issues new ID's needs to know how to do the Verhoeff calculations, and the complexity issue is mitigated."

Can someone more knowledgable try to explain it better? The first sentence sounds like the reason why to use a check digit in the first place. 193.12.151.160 (talk) —Preceding comment was added at 16:27, 7 March 2008 (UTC)[reply]