August  2009, 3(3): 219-226. doi: 10.3934/amc.2009.3.219

On the Fourier spectra of the infinite families of quadratic APN functions


Department of Mathematics, National University of Ireland Maynooth, Co. Kildare, Ireland


School of Mathematical Sciences, Luoyang Normal University, Luoyang 471022, China

Received  November 2008 Revised  July 2009 Published  August 2009

It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the quadrinomial family of APN functions from [5]. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.
Citation: Carl Bracken, Zhengbang Zha. On the Fourier spectra of the infinite families of quadratic APN functions. Advances in Mathematics of Communications, 2009, 3 (3) : 219-226. doi: 10.3934/amc.2009.3.219

Li Zhang, Xiaofeng Zhou, Min Chen. The research on the properties of Fourier matrix and bent function. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 571-578. doi: 10.3934/naco.2020052


Gary Froyland, Cecilia González-Tokman, Anthony Quas. Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 2014, 1 (2) : 249-278. doi: 10.3934/jcd.2014.1.249


Sergiu Aizicovici, Nikolaos S. Papageorgiou, V. Staicu. The spectrum and an index formula for the Neumann $p-$Laplacian and multiple solutions for problems with a crossing nonlinearity. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 431-456. doi: 10.3934/dcds.2009.25.431


Sergey P. Degtyarev. On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions. Evolution Equations & Control Theory, 2015, 4 (4) : 391-429. doi: 10.3934/eect.2015.4.391


Claude Carlet. Revisiting some results on APN and algebraic immune functions. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021035


C. T. Cremins, G. Infante. A semilinear $A$-spectrum. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 235-242. doi: 10.3934/dcdss.2008.1.235


Moises Delgado, Heeralal Janwa. Some new results on the conjecture on exceptional APN functions and absolutely irreducible polynomials: The gold case. Advances in Mathematics of Communications, 2017, 11 (2) : 389-396. doi: 10.3934/amc.2017033


Dmitry Dolgopyat, Dmitry Jakobson. On small gaps in the length spectrum. Journal of Modern Dynamics, 2016, 10: 339-352. doi: 10.3934/jmd.2016.10.339


Natalija Sergejeva. On the unusual Fucik spectrum. Conference Publications, 2007, 2007 (Special) : 920-926. doi: 10.3934/proc.2007.2007.920


Evan Greif, Daniel Kaplan, Robert S. Strichartz, Samuel C. Wiese. Spectrum of the Laplacian on regular polyhedra. Communications on Pure & Applied Analysis, 2021, 20 (1) : 193-214. doi: 10.3934/cpaa.2020263


Umesh V. Dubey, Vivek M. Mallick. Spectrum of some triangulated categories. Electronic Research Announcements, 2011, 18: 50-53. doi: 10.3934/era.2011.18.50


Tim Alderson, Alessandro Neri. Maximum weight spectrum codes. Advances in Mathematics of Communications, 2019, 13 (1) : 101-119. doi: 10.3934/amc.2019006


Emmanuel Schenck. Exponential gaps in the length spectrum. Journal of Modern Dynamics, 2020, 16: 207-223. doi: 10.3934/jmd.2020007


J. Douglas Wright. On the spectrum of the superposition of separated potentials.. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 273-281. doi: 10.3934/dcdsb.2013.18.273


David Damanik, Anton Gorodetski. The spectrum of the weakly coupled Fibonacci Hamiltonian. Electronic Research Announcements, 2009, 16: 23-29. doi: 10.3934/era.2009.16.23


Yves Guivarc'h. On the spectrum of a large subgroup of a semisimple group. Journal of Modern Dynamics, 2008, 2 (1) : 15-42. doi: 10.3934/jmd.2008.2.15


Frédéric Naud. The Ruelle spectrum of generic transfer operators. Discrete & Continuous Dynamical Systems, 2012, 32 (7) : 2521-2531. doi: 10.3934/dcds.2012.32.2521


Tao Yu, Guohua Zhang, Ruifeng Zhang. Discrete spectrum for amenable group actions. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5871-5886. doi: 10.3934/dcds.2021099


Kyril Tintarev. Is the Trudinger-Moser nonlinearity a true critical nonlinearity?. Conference Publications, 2011, 2011 (Special) : 1378-1384. doi: 10.3934/proc.2011.2011.1378


Jiecheng Chen, Dashan Fan, Lijing Sun. Asymptotic estimates for unimodular Fourier multipliers on modulation spaces. Discrete & Continuous Dynamical Systems, 2012, 32 (2) : 467-485. doi: 10.3934/dcds.2012.32.467

2020 Impact Factor: 0.935


  • PDF downloads (86)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]