Editing Check digit (section)

=== NCDA ===
The NOID Check Digit Algorithm (NCDA),<ref>{{Cite web |last=Kunze |first=John A.|title=noid - Nice Opaque Identifier Generator commands |url=https://metacpan.org/dist/Noid/view/noid |url-status=live |archive-url=https://web.archive.org/web/20220522061129/https://metacpan.org/dist/Noid/view/noid |archive-date=2022-05-22 |access-date=2022-10-15 |website=metacpan.org}}</ref> in use since 2004, is designed for application in [[persistent identifier]]s and works with variable length strings of letters and digits, called extended digits. It is widely used with the [[ARK identifier]] scheme and somewhat used with schemes, such as the [[Handle System]] and [[Digital object identifier|DOI]]. An extended digit is constrained to [[wikt:betanumeric|betanumeric]] characters, which are alphanumerics minus vowels and the letter 'l' (ell). This restriction helps when generating opaque strings that are unlikely to form words by accident and will not contain both O and 0, or l and 1. Having a prime radix of R=29, the betanumeric repertoire permits the algorithm to guarantee detection of single-character and transposition errors<ref>David Bressoud, Stan Wagon, "Computational Number Theory", 2000, Key College Publishing</ref> for strings less than R=29 characters in length (beyond which it provides a slightly weaker check). The algorithm generalizes to any character repertoire with a prime radix R and strings less than R characters in length.