McEliece Public Key Encryption The definition of Public Key Encryption(PKE) say that:


  A PKE scheme is a triple of probabilistic polynomial time algorithm (PPT) (Gen,Enc,Dec).


The definition of PPT say:


  In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances.


Let "Find a pair key $(pk,sk)$ (public and private key)" be the problem related with the first algorithm (Gen). In the McEliece scheme, what is a example of error of any instance of the algorithm Gen? Which will be a response "No" and What is a difference between the response "No" and the error response of the algorithm Gen?
A decision problem is to decide if something is true or not (typically phrased in terms of membership of a language). In complexity theory, decision problems are useful for understanding, and most problems can be reduced to a decision problem of some form.

However, in everyday life we are usually not trying to solve decision problems. The algorithms in a public key cryptosystem aren't trying to solve decision problems, so you cannot use the language of decision problems. It just doesn't make sense, as you have discovered.

The notion of polynomial time still makes sense, though.