Small-bias sample space

In theoretical computer science, a small-bias sample space (also known as ${\displaystyle \epsilon }$-biased sample space, ${\displaystyle \epsilon }$-biased generator, or small-bias probability space) is a probability distribution that fools parity functions. In other words, no parity function can distinguish between a small-bias sample space and the uniform distribution with high probability, and hence, small-bias sample spaces naturally give rise to pseudorandom generators for parity functions.

The main useful property of small-bias sample spaces is that they need far fewer truly random bits than the uniform distribution to fool parities. Efficient constructions of small-bias sample spaces have found many applications in computer science, some of which are derandomization, error-correcting codes, and probabilistically checkable proofs. The connection with error-correcting codes is in fact very strong since ${\displaystyle \epsilon }$-biased sample spaces are equivalent to ${\displaystyle \epsilon }$-balanced error-correcting codes.

...
Wikipedia