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arXiv · 1106.5860

On the Statistical Independence of Shift-Register Pseudorandom Multisequence over Part of the Period

Mordechay B. Levin·Irina L. Volinsky
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Abstract

In this paper we construct a pseudorandom multisequence $(x_{n_1,...,n_r})$ based on $k$th-order linear recurrences modulo $p$, such that the discrepancy of the $s$-dimensional multisequence $(x_{n_1+i_1,...,n_r+i_r})_{1 \leq i_j \leq s_j, 1 \leq j \leq r}$ $1 \leq n_j \leq N_j, 1 \leq j \leq r$ is equal to $O((N_1 ... N_r)^{-1/2} \ln^{s+3r}(N_1 ... N_r))$, where $s=s_1 ... s_r$, for all $N_1,...,N_r$ with $1 < N_1 ... N_r \leq p^k

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Mordechay B. Levin, Irina L. Volinsky. 2011-06-29. On the Statistical Independence of Shift-Register Pseudorandom Multisequence over Part of the Period. https://arxiv.org/abs/1106.5860

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