A string of bits is random if and only if it is shorter than any computer program than can produce the string (Kolmogorov Randomness). This means that random strings can not be compressed.
But a scalable algorithm may produce an incomprensible sequence that mimics randonmnes for any length and period we want. But the fact that is incompresible does not mean its random: this is the case of any irrational number like pi, which is deterministic.
Randonmness talks about how likely is some future event to take place. That property was called ‘probability’ by Bernoulli in the 17th century.