Verhoeff algorithm

The Verhoeff algorithm[1] is a checksum for error detection first published by Dutch mathematician Jacobus Verhoeff in 1969.[2][3] It was the first decimal check digit algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,[4] which was at the time thought impossible with such a code.

The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to any base.[5]

  1. ^ Cite error: The named reference Verhoeff_1969 was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference Kirtland_2001 was invoked but never defined (see the help page).
  3. ^ Cite error: The named reference Salomon_2005 was invoked but never defined (see the help page).
  4. ^ Cite error: The named reference Haunsperger_2006 was invoked but never defined (see the help page).
  5. ^ Gumm, H. (January 1985). "A new class of check-digit methods for arbitrary number systems (Corresp.)". IEEE Transactions on Information Theory. 31 (1): 102–105. doi:10.1109/TIT.1985.1056991.