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Cryptology

The Inner Coincidence Index of a Text

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Definition

Let a be a text of length r (r ≥ 2), and κ1(a), ..., κr-1(a) be its autocoincidence spectrum. Then the mean value

φ(a) := [κ1(a) + ... + κr-1(a)] / [r - 1]
is called the (inner) coincidence index of a.


Another Description

In the mathematical background part of this section we prove the Kappa-Phi Theorem: The Coincidence index of a text a is the proportion of coincidences among all letter pairs of a.

This means we run through all the pairs of letters from a and count how many coincidences we find. This number is divided by the number r(r-1)/2 of all letter pairs.

Example: The text

      PAIRSOFLETTERS
has the length r = 14, hence 14x13/2 = 91 letter pairs. Among these are one pair of R, one pair of S, one pair of E, one pair of T, together four coincidences. Therefore φ(a) = 4/91 ≈ 0.044

Remarks:


Author: Klaus Pommerening, 2000-Feb-24; last change: 2013-Oct-26.