# Linear complexity over F-q and over F-qm for linear recurring sequences

2009-02-01
MEİDL, WİLFRİED
Özbudak, Ferruh
Since the F-q-linear spaces F-q(m) and F-qm are isomorphic, an m-fold multisequence S over the finite field F-q with a given characteristic polynomial f is an element of F-q[x], can be identified with a single sequence S over F-qm with characteristic polynomial f. The linear complexity of S, which will be called the generalized joint linear complexity of S, can be significantly smaller than the conventional joint linear complexity of S. We determine the expected value and the variance of the generalized joint linear complexity of a random m-fold multisequence S with given minimal polynomial. The result on the expected value generalizes a previous result oil periodic m-fold multisequences. Moreover we determine the expected drop of linear complexity of a random m-fold multisequence with given characteristic polynomial f, when one switches from conventional joint linear complexity to generalized joint linear complexity.
FINITE FIELDS AND THEIR APPLICATIONS

# Suggestions

 Compact-like operators in lattice-normed spaces Aydın, Abdullah; Emel’yanov, Eduard; Department of Mathematics (2017) Let \$(X,p,E)\$ and \$(Y,m,F)\$ be two lattice-normed spaces. A linear operator \$T:Xto Y\$ is said to be \$p\$-compact if, for any \$p\$-bounded net \$x_alpha\$ in X, the net \$Tx_alpha\$ has a \$p\$-convergent subnet in Y. That is, if \$x_alpha\$ is a net in X such that there is a \$ein E_+\$ satisfying \$p(x_alpha) ≤ e\$ for all \$alpha\$, then there exists a subnet \$x_{alpha_beta}\$ and \$y_in Y\$ such that \$m(Tx_{alpha_beta} −y) xrightarrow{o}0\$ in \$F\$. A linear operator \$T:Xto Y\$ is called \$p\$-continuous if \$p(x_alpha) xrightar...
 Drinfeld modular curves with many rational points over finite fields Cam, Vural; Özbudak, Ferruh; Department of Mathematics (2011) In our study Fq denotes the finite field with q elements. It is interesting to construct curves of given genus over Fq with many Fq -rational points. Drinfeld modular curves can be used to construct that kind of curves over Fq . In this study we will use reductions of the Drinfeld modular curves X_{0} (n) to obtain curves over finite fields with many rational points. The main idea is to divide the Drinfeld modular curves by an Atkin-Lehner involution which has many fixed points to obtain a quotient with a b...
 Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves Özbudak, Ferruh; Saygi, Zulfukar (2012-03-01) Let F-q be a finite field containing F-4. Let k >= 2 be an integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. As an application of this we obtain new results on the classification of maximal and minimal curves over F-q(k) . We also give some nonexistence results on certain systems of equations over F-q(k).
 Quadratic forms of codimension 2 over certain finite fields of even characteristic Özbudak, Ferruh; Saygi, Zulfukar (2011-12-01) Let F-q be a finite field of characteristic 2, not containing F-4. Let k >= 2 be an even integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. We apply this to the classification of maximal and minimal curves over finite fields.
 Homoclinical structure of the chaotic attractor Akhmet, Marat (2010-04-01) In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009:14:1486-93.], a relay system was introduced, which admits a chaotic attractor with Devaney's ingredients. Now, we prove that the attractor consists of homo-clinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Se...
Citation Formats
W. MEİDL and F. Özbudak, “Linear complexity over F-q and over F-qm for linear recurring sequences,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 110–124, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33342. 