Hi,
I just started learning code theory and in class he talked about UD codes.
In class we defined a UD code as one such that every distinct
concatenation of n codewords is distinct for every n; in other words, if
\[x_1 ... x_n \] \[\neq\] \[ y_1 ... y_n,\]
then
\[C(x_1) ... C(x_n) \neq\] \[ C(y_1) ... C(y_2)\]
for every n.
Then in class the professor mentioned a stronger proof of this which makes more
sense to determine a UD code.
if \[x_1 ... x_m \neq\] \[y_1 ... y_n,\]
then
\[C(x_1) ... C(x_m)\neq\] \[C(y_1) ... C(y_2)\]
for every m,n.
The stronger def is easier to define a UD code for example,
A 0
B 11
C 011
AB(011) = C(011) hence it is not UD but with the weak def of UD I am not so sure.
It was later mentioned that the weaker definition implies the stronger definition and I don't see how this works?