Yes! And you can make them as complex as you'd like, and even have custom solution keys!
A couple codes that I messed around with a bit in school are collaborations between me and a couple friends.
The first is like this. Each number is whatever it is on the list. 1-9 for the first two, 1-8 for the third (26 letters in the alphabet).
* = (A->I)
+ = (I->A)
' = (I->Q)
- = (Q->I)
, = (R->Z)
_ = (Z->R)
*85'4-6'7= Hello.
There are two lists for every 'section' of alphabet to avoid doubles. We'd have two symbols for every section, and one symbol would be normal (a=1 b=2 c=3) and then the other would simply be reversed (c=1 b=2 a=3) so that if we had doubles (Hello is a good example) we'd just use the reverse list.
Granted, we didn't use those symbols... we had our own little symbols (which I forget). Anyways, the code worked well. And it's simple to use. We had the lists memorized (which letter was which number) but you could just as easily carry the 'formula' on a piece of paper.
edit: Here's a diagram if you don't get it.
*
a b c d e f g h i = 1 2 3 4 5 6 7 8 9
+
i h g f e d c b a = 1 2 3 4 5 6 7 8 9
And you just put the symbol in front so you know which list to use... and if you have two letters from the same list just put the symbol once... for an example see "Hello" above. H and e are on the same list... so one symbol is used. But in the case of the same letter twice like an L following another l... you want to avoid doubles so you'd use the reverse list.
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