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![The functional graph G(g/F97)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {G}}(g / {\mathbb {F}}_{97})$$\end{document}](publication/376081164/figure/fig3/AS:11431281240332562@1714701611657/The-functional-graph-Gg-F97documentclass12ptminimal-usepackageamsmath.png)
The functional graph G(g/F97)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {G}}(g / {\mathbb {F}}_{97})$$\end{document}
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![The connected component of G(g/F181)\documentclass[12pt]{minimal}...](publication/376081164/figure/fig1/AS:11431281240304994@1714701611211/The-connected-component-of-Gg-F181documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The conneted components of G(g/F181)\documentclass[12pt]{minimal}...](publication/376081164/figure/fig2/AS:11431281240304995@1714701611420/The-conneted-components-of-Gg-F181documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The functional graph G(g/F97)\documentclass[12pt]{minimal}...](publication/376081164/figure/fig3/AS:11431281240332562@1714701611657/The-functional-graph-Gg-F97documentclass12ptminimal-usepackageamsmath_Q320.jpg)
Let Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_q$$\end{document} be a finite field with q elements and let n be a positive integer. In this paper, we...
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The Joux-Vitse Crossbred algorithm's aim is to efficiently solve a system of semi-regular multivariate polyno-mials equations. The authors tested their algorithm for boolean polynomials in F2 and stated that this algorithm also works for other non-boolean finite fields. In addition, the algorithm is dependent on a set of parameters that control its...
Citations
... For each element α ∈ F q ν , we define f −1 (α) = {γ ∈ F q ν | f (γ) = α} and Fix(f ) = {α ∈ F q ν | f (α) = α} as the set of pre-images of α and the set of fixed points of f, respectively. We will introduce some graph notation as in [1,2,11,13,14]. Let m and n be positive integers. ...
... In [17], Ugolini studied rational maps induced by endomorphisms of ordinary elliptic curves. Recently, in [1], Alves J. and Brochero F. studied the digraph associated to the map ...
... For example, Theorem 2.4 can be seen as a particular case of [1, Theorem 2.4]. Also, the authors presented results about the connected components that do not contain zero in [1, Theorem 2.7], but we observe that this result is not applicable when n = 1.Therefore, Theorem 2.11 is not a consequence of[1, Theorem 2.7]. This remark is independent of the parity of q. ...
Let be the finite field with q elements. In this paper we will describe the dynamics of the map with over the finite field .
The complex dynamics of the baker’s map and its variants in infinite-precision mathematical domains and quantum settings have been extensively studied over the past five decades. However, their behavior in finite-precision digital computing remains largely unknown. This paper addresses this gap by investigating the graph structure of the generalized two-dimensional baker’s map and its higher-dimensional extension, referred to as HDBM, as implemented on the discrete setting in a digital computer. We provide a rigorous analysis of how the map parameters shape the in-degree bounds and distribution within the functional graph, revealing fractal-like structures intensify as parameters approach each other and arithmetic precision increases. Furthermore, we demonstrate that recursive tree structures can characterize the functional graph structure of HDBM in a fixed-point arithmetic domain. Similar to the 2-D case, the degree of any non-leaf node in the functional graph, when implemented in the floating-point arithmetic domain, is determined solely by its last component. We also reveal the relationship between the functional graphs of HDBM across the two arithmetic domains. These findings lay the groundwork for dynamic analysis, effective control, and broader application of the baker’s map and its variants in diverse domains.
