Skip to Main content Skip to Navigation
Conference papers

A Lower Bound for the Nonlinearity of Exponential Welch Costas Functions

Abstract : We study the nonlinearity of Exponential Welch Costas functions using the Fourier transform on Zn. Exponential Welch Costas functions are bijections from Zp-1 to Zp-1 defined using the exponential function of Zp, where p is an odd prime. Their linearity properties were recently studied by Drakakis, Requena, and McGuire, who conjectured that the absolute values of the Fourier coefficients of an Exponential Welch Costas function are bounded from above by O(p0,5+ ∈), where ∈ is a small constant. In this paper, we establish an upper bound of order O(√p log p), which is asymptotically strictly less than the bound conjectured by Drakakis et al.
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download

https://hal.inria.fr/inria-00614457
Contributor : Marie Trape <>
Submitted on : Thursday, August 11, 2011 - 2:48:54 PM
Last modification on : Thursday, November 26, 2020 - 2:56:03 PM
Long-term archiving on: : Monday, November 12, 2012 - 3:18:10 PM

File

52.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00614457, version 1

Collections

Citation

Risto Hakala. A Lower Bound for the Nonlinearity of Exponential Welch Costas Functions. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.397-404. ⟨inria-00614457⟩

Share

Metrics

Record views

161

Files downloads

154