# General Report on Tunny

22W Page 73

If is a letter of n dots and m crosses
 P(ΔΨ'a + ΔΨ'b = | TMa = ., TMb = .) = = 1, m = 0 (W1) 0, m ≠ 0
 P(ΔΨ'a + ΔΨ'b = | TMa = ., TMb = x) = = (W2)
 P(ΔΨ'a + ΔΨ'b = | TMa = x, TMb = x) = = (W3)
 and P(ΔΨ'a + ΔΨ'b = ) = (1 - a)2 + 2a(1 - a) + a2 = (W4)

Because limitation (L) is equivalent to ΔΨ'b + x,
 P(ΔΨ'a + ΔΨ'b = | La + Lb = .)  = P(ΔΨ'a +ΔΨ'b = | P(ΔΨ'a +ΔΨ'b = ) = = 2P(ΔΨ'a +ΔΨ'b = ) (W5)
 Similarly P(ΔΨ'a + ΔΨ'b = | La + Lb = x) = 2P(ΔΨ'a +ΔΨ'b = ) (W6)

The following table (for m + n = 5) is constructed, with the aid of W1, 2, 3, 4, 5, 6, in the same way as the table in the last section and gives deciban scores per letter and is used for scoring possible positions for go-backs. Scores for intermediate dottages can be interpolated.

La + Lb = dot La + Lb = cross Dottages
1518212427
Number of dots(n)
 5 4 3 2 1 0 -
 - 5 4 3 2 1 0
 +5½ -1 -1 -1 0 +½ +2
 +7 -1 -1 -1 0 +1 +3½
 +8 - -1 -2 - +2 +5
 +9 - -2 -2 -1 +2½ +7
 +10½ +½ -2 -5 -2 +3 +8½

Fig. (XV)

(c) The sum of two key streams.

It has been suggested that in cases where there are two stretches of Z with the same P it might be possible to find the relative positions of the P, even if neither messages has been decoded for ΔZa + ΔZb = ΔKa + ΔKb

 (W8)