Yes and no. Empty matrix is represented by [[]] array

Yes, kata's description is shit, but IMO this is its greatest advantage. In real life you also will have to fuck with shitty documentation and orders ("shitty" is kinda redundant, because it is implied by word "documentation" :P).

Here plaintext letters are from 'a' to 'z' or from 'A' to 'Z'.

I think that this should be indicated in kata describtion. Also, "latin letter" suits here better than "plaintext letter"

I would recommend reading about character encodings

https://www.joelonsoftware.com/2003/10/08/the-absolute-minimum-every-software-developer-absolutely-positively-must-know-about-unicode-and-character-sets-no-excuses/
https://utf8everywhere.org

Why did you include <string>, <stdio.h> and <math.h>?