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We consider a bound on the bias reduction of a random number generator by processing based on binary linear codes. We introduce a new bound on the total variation distance of the processed output based on the weight distribution of the code generated by the chosen binary matrix. Starting from this result we show a lower bound for the entropy rate of the… (More)

Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily optimal codes. In this paper we identify code parameters (q, d, k), namely field size, minimum distance and combinatorial dimension, for which the Griesmer bound holds also in… (More)

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… (More)

Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family of systematic nonlinear codes for which the Gries-mer bound holds. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit… (More)

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