Quadratic functions with prescribed spectra

Meidl, Wilfried and Topuzoğlu, Alev (2013) Quadratic functions with prescribed spectra. Designs, Codes and Cryptography (SI), 66 (1-3). pp. 257-273. ISSN 0925-1022 (Print) 1573-7586 (Online)

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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.
Item Type: Article
Uncontrolled Keywords: Quadratic Boolean functions; Quadratic p-ary functions; Plateaued functions; Semi-bent functions; Self-reciprocal polynomials; Linear complexity
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Wilfried Meidl
Date Deposited: 12 Feb 2013 11:39
Last Modified: 01 Aug 2019 10:08
URI: https://research.sabanciuniv.edu/id/eprint/21396

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