Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class
Date
2010-04-01
Author
Kavut, Selcuk
Diker, Melek
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
87
views
0
downloads
Cite This
We give a new lower bound to the covering radius of the first order Reed-Muller code RM(1, n), where n is an element of {9, 11, 13}. Equivalently, we present the n-variable Boolean functions for n is an element of {9,11,13} with maximum nonlinearity found till now. In 2006, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel. To improve this nonlinearity result, we have firstly defined some subsets of the n-variable Boolean functions as the generalized classes of "k-RSBFs and k-DSBFs (k-Dihedral Symmetric Boolean Functions)", where k is a positive integer dividing n. Secondly, utilizing a steepest-descent like iterative heuristic search algorithm, we have found 9-variable Boolean functions with nonlinearity 242 within the classes of both 3-RSBFs and 3-DSBFs. Thirdly, motivated by the fact that RSBFs are invariant under a special permutation of the input vector, we have classified all possible permutations up to the linear equivalence of Boolean functions that are invariant under those permutations.
Subject Keywords
Boolean Functions
,
Combinatorial Problems
,
Cryptography
,
Dihedral Symmetry
,
Nonlinearity
,
Rotational Symmetry
URI
https://hdl.handle.net/11511/32541
Journal
INFORMATION AND COMPUTATION
DOI
https://doi.org/10.1016/j.ic.2009.12.002
Collections
Graduate School of Natural and Applied Sciences, Article
Suggestions
OpenMETU
Core
Approximate Pseudospin and Spin Solutions of the Dirac Equation for a Class of Exponential Potentials
Arda, Altug; Sever, Ramazan; TEZCAN, CEVDET (2010-02-01)
The Dirac equation is solved for some exponential potentials the hypergeometric-type potential, the generalized Morse potential, and the Poschl-Teller potential with any spin-orbit quantum number kappa in the case of spin and pseudospin symmetry. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations and the corresponding wave functions are obtained by using a generalization of the Nikiforov-Uvarov method.
Yang-Mills solutions on Euclidean Schwarzschild space
Tekin, Bayram (2002-04-15)
We show that the apparently periodic Charap-Duff Yang-Mills "instantons" in time-compactified Euclidean Schwarzschild space are actually time independent. For these solutions, the Yang-Mills potential is constant along the time direction (no barrier) and therefore, there is no tunneling. We also demonstrate that the solutions found to date are three-dimensional monopoles and dyons. We conjecture that there are no time-dependent solutions in the Euclidean Schwarzschild background.
Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
On the number of topologies on a finite set
Kızmaz, Muhammet Yasir (2019-01-01)
We denote the number of distinct topologies which can be defined on a set X with n elements by T(n). Similarly, T-0(n) denotes the number of distinct T-0 topologies on the set X. In the present paper, we prove that for any prime p, T(p(k)) k+ 1 (mod p), and that for each natural number n there exists a unique k such that T(p + n) k (mod p). We calculate k for n = 0, 1, 2, 3, 4. We give an alternative proof for a result of Z. I. Borevich to the effect that T-0(p + n) T-0(n + 1) (mod p).
On local finiteness of periodic residually finite groups
Kuzucouoglu, M; Shumyatsky, P (2002-10-01)
Let G be a periodic residually finite group containing a nilpotent subgroup A such that C-G (A) is finite. We show that if [A, A(g)] is finite for any g is an element of G, then G is locally finite.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Kavut and M. Diker, “9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class,”
INFORMATION AND COMPUTATION
, pp. 341–350, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32541.