In this paper, 2-adic complexity of two classes generalized cyclotomic binary sequences is investigated. The in the first class have period <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="eq-00001.gif"><mml:mrow><mml:mi>p</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, and their attains maximum, where both p...

Using the cyclotomic classes and generalized for sequence design is a well known method. In this paper, we study symmetric 2-adic complexity of sequences based on order two. These with period 2p^n have high linear complexity. We show that these good enough to resist attack rational approximation algorithm. The measure predictability which important cryptographic applications. Our method studying using “Gauss periods”.

Automatic sequences such as the Thue–Morse sequence and Rudin–Shapiro are highly predictable thus not suitable in cryptography. In particular, they have small expansion complexity. However, still a large maximum order Certain subsequences of automatic anymore may be attractive candidates for applications this paper we show that along squares certain pattern including also complexity but do suffer anymore.

The nonlinear complexity of a periodic sequence s is the length shortest feedback shift register that can generate s, and its value upper bounded by least period minus 1. In this paper, recursive approach generates all sequences with maximum presented, total number such determined. randomness properties these are also examined.

Abstract Expansion complexity and maximum order are both finer measures of pseudorandomness than the linear which is most prominent quality measure for cryptographic sequences. The expected value N th magnitude log whereas it easy to find families sequences with expansion exponential in . This might lead conjecture that a complexity. However, this paper we provide two examples, Thue-Morse sequence Rudin-Shapiro very small but large More precisely, prove explicit formulas their largest...

Finite length sequences with large nonlinear complexity over $\mathbb{Z}_{p}\, (p≥ 2)$ are investigated in this paper. We characterize all $p$-ary of $n$ having $n-j$ for $j=2, 3$, where is an integer satisfying $n≥ 2j$. For 8$, binary $n-4$ obtained. Furthermore, the numbers and $k$-error these completely determined, respectively.

Triple-cycle permutations over finite fields of characteristic two are studied, and some classes triple-cycle proposed in this paper. In addition, new can be constructed by switching construction from known ones.

In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half length investigated. By characterizing structure sequences, an algorithm proposed to generate all with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> and notation="LaTeX">$c\geq n/2$ , where integer larger 2. Furthermore, a formula established calculate exact...

&lt;p style='text-indent:20px;'&gt;In this paper, we characterize all nonbinary sequences of length &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ n $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; with nonlinear complexity id="M3"&gt;\begin{document}$ n-4 for id="M4"&gt;\begin{document}$ n\geq9 and establish a formula on the number such sequences. More generally, other finite large over id="M5"&gt;\begin{document}$ \mathbb{Z}_{m}...

Abstract. In this paper, we study the symmetric 2-adic complexity of generalized cyclotomic sequences with period 2𝑝 𝑛. These are based on binary classes order two and have high linear complexity. The is another measure predictability a sequence thus its unsuitability for cryptography. We prove that considered attains maximal value. “Gauss periods” used to derive these

Foreground-conditioned inpainting aims to seamlessly fill the background region of an image by utilizing provided foreground subject and a text description. While existing T2I-based methods can be applied this task, they suffer from issues shape expansion, distortion, or impaired ability align with description, resulting in inconsistencies between visual elements To address these challenges, we propose Pinco, plug-and-play foreground-conditioned adapter that generates high-quality...

For an integer q≥2, new sets of q-phase aperiodic complementary sequences (ACSs) are constructed by using known ACSs and certain matrices. Employing the Kronecker product to two ACSs, some with a length obtained. even q, parameters generated, their equivalent matrix representations also presented.

Expansion complexity and maximum order are both finer measures of pseudorandomness than the linear which is most prominent quality measure for cryptographic sequences. The expected value $N$th magnitude $\log N$ whereas it easy to find families sequences with expansion exponential in N$. This might lead conjecture that a complexity. However, this paper we provide two examples, Thue-Morse sequence Rudin-Shapiro very small but large More precisely, prove explicit formulas their largest...

The expansion complexity is a new figure of merit for cryptographic sequences. In this paper, we present an explicit formula the (irreducible) ultimately periodic sequences over finite fields. We also provide improved upper and lower bounds on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> th irreducible when they are not explicitly determined. addition, some infinite with...

We study the minimal realization of a low dimension SISO linear system in max-algebra. classify 3-rank periodic unit impulse response sequence {g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> } xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <sup xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> into four categories according to their characteristic equations, and discuss necessary sufficient conditions existence 3D respectively.

Automatic sequences such as the Thue-Morse sequence and Rudin-Shapiro are highly predictable thus not suitable in cryptography. In particular, they have small expansion complexity. However, still a large maximum order Certain subsequences of automatic anymore may be attractive candidates for applications this paper we show that along squares certain pattern including also complexity but do suffer anymore.