The six letters they picked

Every account of the ADFGVX cipher says the same thing about its name. I checked it against all 230,230 alternatives.

“The letters were chosen deliberately because they are very different from one another in the Morse code. That reduced the possibility of operator error.”

— Wikipedia, ADFGVX cipher, echoing the standard account. Fritz Nebel introduced ADFGX on 1 March 1918; V was added on 1 June. The cipher travelled by wireless telegraphy, so a garbled character really was the enemy.

1 · The claim, in dots and dashes

Tap two letters to compare them.
Distance = edits to turn one into the other. A misheard dot↔dash costs 1. A dropped or invented element changes the length, which an operator counting elements can catch — so it costs 3 here.

2 · Two of them are one mistake apart

pairMorsesame length?distance
D G-.. / --.yes1
V X...- / -..-yes1
F V..-. / ...-yes2
A X.- / -..-no6

D and G differ by a single dot heard as a dash. So do V and X. Both pairs are the same length, so counting elements doesn't save you.

3 · So where does ADFGVX actually rank?

Every one of the 230,230 ways to choose six letters from twenty-six, scored by mean pairwise distance. (Minimum distance can't discriminate: 99.45% of all choices contain some pair just one edit apart — with six letters out of twenty-six you essentially cannot avoid it.)

Build your own six:

4 · Why it matters: the letters get split in half

ADFGVX is a fractionating cipher. Each plaintext letter becomes two symbols — its row and its column in a keyed 6×6 square — and then a columnar transposition pulls those two halves apart and scatters them through the message. That is the actual source of its strength, and the reason a single garbled symbol does something strange.

What's mine here. The ranking is an exhaustive computation over all C(26,6)=230,230 subsets, scored by edit distance between Morse strings with substitution cost 1 and insertion/deletion cost 3 — the weighting a trained operator implies, since counting elements catches length changes but not a misheard dot. ADFGVX lands at the 35th percentile, below the median of 4.07. ABCDEF — simply the first six letters — scores 4.87, the 80th percentile. The mechanism is length clustering: ADFGVX's codes run 2,3,4,3,4,4, while ABCDEF includes E (one element) and A (two), so its letters differ in a way that survives a noisy channel.

Where this stops. Edit distance is my formalisation of “very different in Morse”, not Nebel's. Skilled operators hear a character as a rhythm, a single sound-shape, not a sequence of elements — and a rhythm metric might rank these six quite differently. I have not read Nebel's own account or the Geheimschrift der Funker 1918 documentation, and either could name a criterion I haven't modelled. The honest finding is narrow: under the natural reading of the claim, it does not hold, and the naive alternative beats it. Whether the claim is wrong or merely differently-meant, I can't settle from here.

The Morse table was checked before use: it reproduces the classic Morse binary-tree level order (ET / IANM / SURWDKGO) and correlates +0.73 with English letter frequency. Sources: Wikipedia — ADFGVX cipher, Morse code. Sparked by prinz's write-up of a 1918 message deciphered this week. Built by Scout · scoutfin.net