It is known that the Morse $A B C$ letters are built from two signals: a dot and a dash. We would like to form a new $A B C$ from these signals under the following considerations:

a) each letter should correspond to a sequence of seven signals;

b) if during communication, one signal in any of our letters is transmitted incorrectly, the letter should still be reliably recognizable.

How many letters can this $A B C$ consist of?
From two symbols, $2^{7}$ different seven-element sequences can be created. If one symbol in any of these is distorted, depending on which symbol is distorted, we get seven new sequences. In a system whose elements are seven-element sequences, and we want to recognize these even after distortion, the sequences obtained by distortion must also be distinct. Since from one sequence, along with its distorted versions, $1+7=2^{3}$ sequences are derived, in a reconstructable system, there can be at most $2^{7}: 2^{3}=2^{4}$ different sequences.

The fact that the number of possibilities is exactly a power of 2 suggests the idea that in the sought sequences, the first few (in this case, 4) symbols can be chosen freely, and the remaining symbols can be selected skillfully to prepare for the detection of possible distortions. If these additional symbols can be uniquely calculated from the initial symbols, then the violation of these rules will lead us to the location of the error.

Let us denote our symbols by 0 and 1, and the $i$-th symbol in a sequence to be constructed by $x_{i}$, and perform the operations modulo 2. Then the following relationships will yield the desired result:

\[
\begin{aligned}
& x_{5}=x_{1}+x_{2}+x_{3} \\
& x_{6}=x_{1}+x_{2} \quad+x_{4} \\
& x_{7}=x_{1}+\quad x_{3}+x_{4}
\end{aligned}
\]

If all these hold in the taken sequence, there is no error. If exactly one of them does not hold, the one that is distorted among $x_{5}, x_{6}, x_{7}$ is the one whose characteristic relationship does not hold. If 2 relationships are invalid, exactly the one among $x_{2}, x_{3}, x_{4}$ is distorted which appears in the invalid relationships. Finally, if all relationships are invalid, $x_{1}$ is distorted. Since we only have two types of symbols, it is enough to find the location of the distortion.

Therefore, in the examined alphabet, 16 letters can appear.