Alessio Meneghetti

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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)
Randomness is of fundamental importance in various fields, such as cryptography, numerical simulations, or the gaming industry. Quantum physics, which is fundamentally probabilistic, is the best option for a physical random number generator. In this article, we will present the work carried out in various projects in the context of the development of a(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)
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)
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)
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