An upper bound for the linearity of Exponential Welch Costas functions

作者：Hakala Risto M^*

来源：Finite Fields and Their Applications, 2012, 18(4): 855-862.

DOI：10.1016/j.ffa.2012.05.001

• Linearity
• Non linearity
• Welch Costas functions
• Exponential function
• Fourier analysis

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+epsilon)), where epsilon is a small constant. We prove that the linearity is upper bounded by 2/pi root p ln p + 4 root p, which is asymptotically strictly less than what was previously conjectured.

• 出版日期2012-7