Quadratic functions with prescribed spectra

Meidl, Wilfried and Topuzoğlu, Alev (2012) Quadratic functions with prescribed spectra. (Accepted/In Press)

WarningThere is a more recent version of this item available.

[img]PDF - Registered users only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader


We study a class of quadratic p-ary functions Fp,n from \F_p^n to F_p, p ≥ 2, which are well-known to have plateaued Walsh spectrum; i.e., for each b ∈ F_p^n the Walsh transform fˆ(b) satisfies |fˆ(b)|^2 ∈ {0, p^(n+s)} for some integer 0 ≤ s ≤ n − 1. For various types of integers n, we determine possible values of s, construct Fp,n with prescribed spectrum, and present enumeration results. Our work generalizes some of the earlier results, in characteristic two, of Khoo et. al. (Des Codes Cryptogr, 38, 279–295, 2006) and Charpin et al. (IEEE Trans Inf Theory 51, 4286–4298, 2005) on semi-bent functions, and of Fitzgerald (Finite Fields Appl 15, 69–81, 2009) on quadratic forms.

Item Type:Article
Uncontrolled Keywords:Quadratic Boolean functions · Quadratic p-ary functions · Plateaued functions · Semi-bent functions · Self-reciprocal polynomials · Linear complexity
ID Code:20022
Deposited By:Wilfried Meidl
Deposited On:09 Nov 2012 22:20
Last Modified:31 Jul 2019 14:15

Available Versions of this Item

Repository Staff Only: item control page