Niho Type Cross-Correlation Functions and Related Equations Niho Type Cross-Correlation Functions and Related Equations
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چکیده
منابع مشابه
On Niho type cross-correlation functions of m-sequences
Assume that d ≡ 1 (mod q − 1). We study the number of solutions to (x + 1)d = xd + 1 in GF(q2). In addition, we give a simple proof of the fact that the cross-correlation function between two m-sequences, which differ by a decimation of this type, is at least four-valued. © 2005 Elsevier Inc. All rights reserved.
متن کامل$p$-ary sequences with six-valued cross-correlation function: a new decimation of Niho type
For an odd prime p and n = 2m, a new decimation d = (p−1) 2 +1 of Niho type ofm-sequences is presented. Using generalized Niho’s Theorem, we show that the cross-correlation function between a p-ary m-sequence of period pn−1 and its decimated sequence by the above d is at most six-valued and we can easily know that the magnitude of the cross correlation is upper bounded by 4 √ p − 1.
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In this paper, let n = 2m and d = 3 − 2 with m ≥ 2 and gcd(d, 3n − 1) = 1. By studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over the finite field F3n , the correlation distribution between a ternarym-sequence of period 3n−1 and its d-decimation sequence is completely determined. This is the first time that the correlation...
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One of the classes of bent Boolean functions introduced by John Dillon in his thesis is family H. While this class corresponds to a nice original construction of bent functions in bivariate form, Dillon could exhibit in it only functions which already belonged to the wellknown Maiorana-McFarland class. We first notice that H can be extended to a slightly larger class that we denote by H. We obs...
متن کاملConstruction of bent functions via Niho power functions
A Boolean function with an even number n = 2k of variables is called bent if it is maximally nonlinear. We present here a new construction of bent functions. Boolean functions of the form f(x) = tr(α1x1 + α2x2), α1, α2, x ∈ F2n , are considered, where the exponents di (i = 1, 2) are of Niho type, i.e. the restriction of xi on F2k is linear. We prove for d1 = 2 + 1 and d2 = 3 · 2k−1 − 1, d2 = 2 ...
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