Quadratic functions with prescribed spectra

Abstract

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.

Available Versions of this Item

• Quadratic functions with prescribed spectra. (deposited 09 Nov 2012 22:20) [Currently Displayed]
  • Quadratic functions with prescribed spectra. (deposited 12 Feb 2013 11:39)