An upper bound for the linearity of Exponential Welch Costas functions
| Autor: | Risto Hakala |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
02 engineering and technology
01 natural sciences Upper and lower bounds Prime (order theory) Theoretical Computer Science Combinatorics symbols.namesake Linearity 0202 electrical engineering electronic engineering information engineering 0101 mathematics Nonlinearity Engineering(all) Computer Science::Information Theory Mathematics Algebra and Number Theory Applied Mathematics Exponential function 010102 general mathematics General Engineering Function (mathematics) Fourier analysis Fourier transform Welch Costas functions Bounded function symbols 020201 artificial intelligence & image processing Bijection injection and surjection |
| Zdroj: | Finite Fields and Their Applications. 18:855-862 |
| ISSN: | 1071-5797 |
| DOI: | 10.1016/j.ffa.2012.05.001 |
| Popis: | The maximum correlation between a function and affine functions is often called the linearity of the function. In this paper, we determine an upper bound for the linearity of Exponential Welch Costas functions using Fourier analysis on Z n . Exponential Welch Costas functions are bijections on Z p − 1 , where p is an odd prime, defined using an exponential function of Z p . Their linearity properties were recently studied by Drakakis, Requena, and McGuire (2010) [1] who conjectured that the linearity of an Exponential Welch Costas function on Z p − 1 is bounded from above by O ( p 0.5 + ϵ ) , where ϵ is a small constant. We prove that the linearity is upper bounded by 2 π p ln p + 4 p , which is asymptotically strictly less than what was previously conjectured. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect