Superimposed code

Many names, some of them trademarked, have been used for marginal punched-card systems: edge-notched cards, slotted cards, E-Z Sort, Zatocards, McBee, McBee Keysort, Flexisort, Velom, Rocket, etc.

The center of each card held the relevant information—typically the name and author of a book, research paper, or journal article on a nearby shelf; and a list of subjects and keywords.

A user could repeat this selection many times to form a complex Boolean searching query.

[1] Once you have a collection of index cards, one per book, research paper, or journal article in a library, with a list of keywords (subjects) discussed in a particular book written on that book's card, the "obvious way" to code those subjects is to count up the total number of subjects used in the entire collection R, make a row of R holes near the top of every card, and for each subject actually discussed in a particular book, cut a slot from the hole corresponding to that subject in the card corresponding to that book.

While it may not seem possible to use less than 1 hole per subject, superimposed code systems can solve this problem.

The Zatocoding system of information retrieval was developed by Calvin Mooers in 1947.

[3] Calvin Mooers invented Zatocoding at M.I.T., a mechanical information retrieval system based on superimposed codes, and formed the Zator Company in 1947 to commercialize its applications.

The probability F of some undesired card with v slots cut in it falling through when we select some pattern of n needles is approximately