Improving results on the pseudorandomness of sequences generated via the additive order of a finite field

Merai, Laszlo
Yayla, Oğuz
We improve several results in the area of pseudorandom sequences. First, we obtain an improved bound on the general lattice test for digital explicit inversive and digital explicit nonlinear pseudorandom number generators. Second, we improve the bound on the correlation measure of binary sequences generated by the quadratic character of finite fields. Finally, we improve the bound on the correlation measure of digital explicit inversive pseudorandom numbers, and the bound on their linear complexity profile.


On Lempel-Ziv complexity of sequences
Doğanaksoy, Ali (2006-01-01)
We derive recurrences for counting the number a(n, r) of sequences of length n with Lempel-Ziv complexity r, which has important applications, for instance testing randomness of binary sequences. We also give algorithms to compute these recurrences. We employed these algorithms to compute a(n, r) and expected value, EPn, of number of patterns of a sequence of length n, for relatively large n. We offer a randomness test based on the algorithms to be used for testing randomness of binary sequences. We give ou...
Applications of estimation techniques on genetic and other types of data
Aslan, Murat; Akkaya, Ayşen; Department of Statistics (2003)
The parameters of genetic and other types of data, particularly with small samples, are estimated by using method of moments, least squares, minimum chi- square, maximum likelihood and modified maximum likelihood estimation methods. These methods are also compared in terms of their efficiencies and robustness property.
Aggregate codifferential method for nonsmooth DC optimization
Tor, Ali Hakan; Bagirov, Adil; Karasözen, Bülent (2014-03-15)
A new algorithm is developed based on the concept of codifferential for minimizing the difference of convex nonsmooth functions. Since the computation of the whole codifferential is not always possible, we use a fixed number of elements from the codifferential to compute the search directions. The convergence of the proposed algorithm is proved. The efficiency of the algorithm is demonstrated by comparing it with the subgradient, the truncated codifferential and the proximal bundle methods using nonsmooth o...
Numerical Improvement of Terahertz Time-Domain Spectroscopic Measurements
Koseoglu, D.; Berberoglu, H.; Altan, Hakan (2009-11-06)
We have developed an algorithm to efficiently eliminate unwanted reflections typically observed in the data obtained by Terahertz time-domain spectroscopic (THz-TDS) methods. The algorithm works by eliminating the reflections from the boundaries. The numerical improvement of the data allows better analysis of the critical parameters obtained by THz-TDS systems.
Improved p-ary codes and sequence families from Galois rings
Ling, San; Özbudak, Ferruh (2005-01-01)
In this paper, a recent bound on some Weil-type exponential sums over Galois rings is used in the construction of codes and sequences. The bound on these type of exponential sums provides a lower bound for the minimum distance of a family of codes over F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m)((D-[D/p2])), where 1 <= D <= p(m/2). Several families of pairwise cyclically distinct p-ary sequences of period p(p(m) - 1) of low correlation are also constructed. They compare favorably with cer...
Citation Formats
L. Merai and O. Yayla, “Improving results on the pseudorandomness of sequences generated via the additive order of a finite field,” DISCRETE MATHEMATICS, pp. 2020–2025, 2015, Accessed: 00, 2020. [Online]. Available: