# American Institute of Mathematical Sciences

doi: 10.3934/amc.2020087

## Correlation distribution of a sequence family generalizing some sequences of Trachtenberg

 1 Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey 2 Department of Business Administration, Karabük University, 78050, Karabük, Turkey 3 Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey

* Corresponding author: Eda Tekin

Received  November 2019 Published  June 2020

In this paper, we give a classification of a sequence family, over arbitrary characteristic, adding linear trace terms to the function $g(x) = \mathrm{Tr}(x^d)$, where $d = p^{2k}-p^k+1$, first introduced by Trachtenberg. The family has $p^n+1$ cyclically distinct sequences with period $p^n-1$. We compute the exact correlation distribution of the function $g(x)$ with linear $m$-sequences and amongst themselves. The cross-correlation values are obtained as $C_{i,j}(\tau) \in \{-1,-1\pm p^{\frac{n+e}{2}},-1+p^n\}$.

Citation: Ferruh Özbudak, Eda Tekin. Correlation distribution of a sequence family generalizing some sequences of Trachtenberg. Advances in Mathematics of Communications, doi: 10.3934/amc.2020087
##### References:

show all references

##### References:
 [1] Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190 [2] Qian Liu. The lower bounds on the second-order nonlinearity of three classes of Boolean functions. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2020136 [3] Davide La Torre, Simone Marsiglio, Franklin Mendivil, Fabio Privileggi. Public debt dynamics under ambiguity by means of iterated function systems on density functions. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021070

2019 Impact Factor: 0.734