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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Official URL: http://dx.doi.org/10.1007/s10623-012-9690-6


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:21396
Deposited By:Wilfried Meidl
Deposited On:12 Feb 2013 11:39
Last Modified:01 Aug 2019 10:08

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