Code generator matrices as entropy extractors

We show the connection between the Walsh spectrum of the output of a binary random number generator (RNG) and the bias of individual bits, and use this to show how previously known bounds on the performance of linear binary codes as entropy extractors can be derived by considering generator matrices as a selector of a subset of that spectrum. We explicitly show the connection with the code's weight distribution, then extend this framework to the case of non-binary finite fields by the Fourier transform.