Code generator matrices as RNG conditioners

TL;DR

This paper analyzes how binary linear code generator matrices influence the distribution of RNG outputs, linking spectral properties to code weight distribution, and extends the framework to non-binary codes.

Contribution

It establishes a precise connection between the Walsh spectrum of conditioned RNG outputs and the code's weight distribution, extending the analysis to non-binary codes.

Findings

Spectral analysis of RNG conditioned by code matrices

Bounds on code performance as entropy extractors

Extension of framework to non-binary codes

Abstract

We quantify precisely the distribution of the output of a binary random number generator (RNG) after conditioning with a binary linear code generator matrix by showing the connection between the Walsh spectrum of the resulting random variable and the weight distribution of the code. 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 also extend this framework to the case of non-binary codes.