In coding theory, 'how good code is' means how many channel errors can be corrected, or better put, the maximal noise level that the code can deal with.

In order to get better codes, the codes are designed using a large alphabet (rather than binary one). And then, the code is good if it can deal with a large rate of erroneous "symbols".

Why isn't this consider cheating? I mean, shouldn't we only care about what happens when we "translate" each symbol into a binary string? The "rate of bit error" is different than the rate of "symbol error". For instance, the rate of bit-error cannot go above 1/2 while (if I understand this correctly), with large enough alphabet, the symbol-error can go up to $1-\epsilon$. Is this because we artificially restrict the channel to change only "symbols" rather than bits, or is it because the code is better actually better?

In coding theory, 'how good a code is' means how many channel errors can be corrected, or better put, the maximal noise level that the code can deal with.

In order to get better codes, the codes are designed using a large alphabet (rather than binary one). And then, the code is good if it can deal with a large rate of erroneous "symbols".

Why isn't this consider cheating? I mean, shouldn't we only care about what happens when we "translate" each symbol into a binary string? The "rate of bit error" is different than the rate of "symbol error". For instance, the rate of bit-error cannot go above 1/2 while (if I understand this correctly), with large enough alphabet, the symbol-error can go up to $1-\epsilon$. Is this because we artificially restrict the channel to change only "symbols" rather than bits, or is it because the code is actually better?