Abstract
We prove a discrepancy bound “on average” over all initial values a α (0)=α of congruential pseudorandom numbers obtained from the sequences a α (n) over a finite field of prime order defined by a α (n)=na α (n–1)+1, n=1,2,..., using new bounds on certain exponential sums.
Moreover, we prove a lower bound on the linear complexity of this sequence showing that its structural properties are close to be best possible.
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Shparlinski, I.E., Winterhof, A. (2006). On the Discrepancy and Linear Complexity of Some Counter-Dependent Recurrence Sequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_25
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DOI: https://doi.org/10.1007/11863854_25
Publisher Name: Springer, Berlin, Heidelberg
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