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After a verification condition generator has created the verification conditions they are passed to an automated theorem prover, which can then formally prove the correctness of the code. Methods have been proposed to use the operational semantics of machine languages to automatically generate verification condition generators. [1]
It can be shown that if is a pseudo-random number generator for the uniform distribution on (,) and if is the CDF of some given probability distribution , then is a pseudo-random number generator for , where : (,) is the percentile of , i.e. ():= {: ()}. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard ...
This, as every polynomial code, is indeed a linear code, i.e., linear combinations of code words are again code words. In a case like this where the field is GF(2), linear combinations are found by taking the XOR of the codewords expressed in binary form (e.g. 00111 XOR 10010 = 10101).