Correlation distribution of a sequence family generalizing some sequences of trachtenberg

Date

2021-08-01

Author

Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

240
views

0
downloads

In this paper, we give a classification of a sequence family, over arbitrary characteristic, adding linear trace terms to the function g(x) = 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,C-j(tau) is an element of {-1, -1 +/- p(n+e/2), -1 + p(n)}.

Subject Keywords

Sequences, Cross-correlation, Plateaued functions

URI

https://hdl.handle.net/11511/92015

Journal

ADVANCES IN MATHEMATICS OF COMMUNICATIONS

DOI

https://doi.org/10.3934/amc.2020087

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Correlation Distribution of a New Sequence Family BOZTAŞ, Serdar; Özbudak, Ferruh; TEKİN, Eda (2015-06-19) In this paper a new binary sequence family with 2(n) + 1 cyclically distinct sequences each having length 2(n) - 1 is presented for an even integer n. The correlation distribution of the family is fully determined. The family has six-valued correlation distribution and its maximum correlation magnitude equals 1 + 2(n/2 + 1).
On plateaued functions, linear structures and permutation polynomials Mesnager, Sihem; Kaytancı, Kübra; Özbudak, Ferruh (2019-01-01) We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some app...
Characterisation and enumeration of a class of semi bent quadratic Boolean functions KOÇAK, Neşe; Koçak, Onur Ozan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2015-01-01) In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Electromagnetic form factors of electrodisintegration of light nuclei near threshold Yalcin, C; Rekalo, MP; Koru, H (1998-06-01) The general structure of electromagnetic currents for electrodisintegration of nuclei near threshold, e(-) + A --> e(-) + A(1) + A(2) (A, A(1) and A(2) are arbitrary nuclei or hadrons with spins 0, 1/2 and 1), are established. Considering nuclei as elementary particles with the definite values of spin and space parity and using the conservation of hadronic electromagnetic current and P-invariance of hadron electromagnetic interaction, the spin structure of the amplitudes of the processes gamma* + A --> A(1)...
Factorization of Joint Probability Mass Functions into Parity Check Interactions Bayramoglu, Muhammet Fatih; Yılmaz, Ali Özgür (2009-07-03) We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors an d factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity chec k equation. In other words, marginalization of a joint PMF is equivalent to a soft decoding task as long as a finite field can be constructed over the alphabet of the PMF. In factor graph terminology this claim means that a factor graph representing such a joint PMF alw...

Citation Formats

F. Özbudak, “Correlation distribution of a sequence family generalizing some sequences of trachtenberg,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 15, no. 4, pp. 647–662, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/92015.