Could anyone share some context around the fascination with the period 19 transformation of z340? I see references to that in many forum posts. From what I understand there is a spike in bigram repeats (37 I think) for period 19 — but are there any other characteristics of period 19 that I might be missing?
One of the reasons I’m curious is because I tested with random columnar transposition keys and can find many keys that result in higher counts (52 or more) of bigram repeats than period 19. My fear is that period 19 is a red herring so to speak, but I feel a bit naive saying that.
(I only joined the forum last week, so I’m not the most experienced to answer but my opinion is..)
Period 19 is a very simple transformation, resulting in a notable spike. It is the highest spike for simple single skip transformations.
With 17 columns, you can rearrange them in 17x16x15x14….x3x2 ways = 17! = 355,687,428,096,000… a huge number…so you are very likely to find some of those arrangements with a high bigram count by chance alone.
In fact, it should be possible to work out the "best" column rearrangement to maximise bigrams. It will be a set of solutions (several all with the same bigram count), and I’m sure someone here has run those looking for homophonic cipher solutions.
CK
I side with cipherkid’s explanation.
– Also, we had never much to go on with the 340 and with the discovery of period 19 it felt like we had a chance to solve it. Perhaps it is a red herring because it has not panned out yet but I still find it interesting and worth my time to work on.
– There is also some period 19 Zynchronity with some of the other stuff surrounding the Zodiac case: viewtopic.php?f=81&t=4503&p=74157#p74154
– And it is very easy to form even more than 37 bigrams (45 bigrams for example) with other simple transformations mixed in: viewtopic.php?f=81&t=3591
– While taking the highest result from period 1 to 170, a bigram peak of 37 or better occurs 1 in 210 randomizations.
– While taking the highest result from offset column order 0 to 16 + period 1 to 170, a bigram peak of 45 or better occurs 1 in 100000 randomizations.
