Correct permutation cycle for Verhoeff algorithm
- by James
Hello,
I'm implementing the Verhoeff algorithm for a check digit scheme, but there seems to be some disagreement in web sources as to which permutation cycle should form the basis of the permutation table.
Wikipedia uses: (36)(01589427)
while apparently, Numerical Recipies uses a different cycle and this book uses: (0)(14)(23)(56789), quoted from a 1990 article by Winters. It also notes that Verhoeff used the one Wikipedia quotes.
Now, my number theory is a little rusty, but the Wikipedia cycle clearly will repeat after the 8th power, while the book one will take 10, despite it saying that s^8=s. Table 2.14(b) has other errors in the 2-cycles, so this is dubious anyway.
Unfortunately, I don't have copies of the original articles (and am too tight to pay/disgusted that 40-year old knowledge is still being held to ransom by publishers), nor a copy of Numerical Recipes to check (and am loath to install their paranoia-induced copy protection plug-in to view online).
So does any one know which is correct? Are they both correct?
