On the constructions of n-cycle permutations
WebPDF Any permutation polynomial is an n-cycle permutation When n is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations These permutations have important applications in cryptography and coding theory Inspired by the AGW Criterion, we … Web21 de jul. de 2024 · For the form of x^rh(x^s), several new explicit triple-cycle permutations are also provided. Finally, we also consider triple-cycle permutations of the form x^t + c Tr_q^m/q(x^s) and provide one explicit construction. Many of our constructions are both new in the n-cycle property and the permutation property. READ FULL TEXT VIEW PDF
On the constructions of n-cycle permutations
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WebA permutation is called a cyclic permutation if and only if it has a single nontrivial cycle (a cycle of length > 1).. For example, the permutation, written in two-line notation (in two ways) and also cycle notation, = = ( ) (),is a six-cycle; its cycle diagram is shown at right. Some authors restrict the definition to only those permutations which consist of one nontrivial … Web23 de ago. de 2016 · In this paper, we generalize the switching method and present a method to construct new differentially 4-uniform permutations from two known ones by determining the corresponding cycle sets. As for applications, by determining all the cycle sets of ( x + 1 ) − 1 + 1 and ( x + 1 ) − 1 + ω related to the inverse functions, respectively, …
Webn is trivial unless n = 6 and the outer automorphism group of Sym 6 has a unique nontrivial element. When we study symmetric groups, we often invoke their natural faithful representation as permutations of a set without a second thought, but to what extent is this representation intrinsic to the structure of the group and Web1 de ago. de 2024 · When n is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle …
WebDe nition 1.2. A cyclic word n is a universal cycle, or u-cycle, for n-permutations if n covers every n-permutation exactly once. 1.4 Organization of the paper This paper is organized as follows. In Section2.1we show our simple way to generate the words 0 n and n, and in Sections2.2and2.3we justify that the constructions of 0 n and n work. Also ... Web22 de set. de 2024 · Throughout the text, q is an odd prime power and \(\chi \in \{-1,1\}\).We study Rédei functions that induce permutations over \(\mathbb {P}^1({\mathbb {F}}_{q})\) whose cycle decomposition contains only cycles of length 1 and j with \(j\ge 2\).We refer to cycles of length j as j-cycles.In addition, whenever we say that a permutation has 1- and …
Web15 de jan. de 2024 · Any Eulerian tour in the cluster graph gives a Hamiltonian cycle in the graph of overlapping n-permutations.It is conjectured that these Hamiltonian cycles can be extended to universal cycles for n-permutations; see [5], [15].. For words, translating a Hamiltonian cycle in the De Bruijn graph to a De Bruijn sequence is straightforward …
Web21 de jul. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … china rummy setgrammarly meme adWeb27 de jul. de 2024 · Based on the Feistel and MISTY structures, this paper presents several new constructions of complete permutation polynomials (CPPs) of the finite field … china running outfitsWeb1 de jan. de 2024 · Involutions over finite fields are permutations whose compositional inverses are themselves. Involutions especially over \( \mathbb {F}_{q} \) with q is even have been used in many applications ... china rugged laptopWebPub Date: July 2024 DOI: 10.48550/arXiv.2207.10491 arXiv: arXiv:2207.10491 Bibcode: 2024arXiv220710491N Keywords: Computer Science - Information Theory; grammarly memeWebWe demonstrate our approaches by constructing three classes of explicit triple-cycle permutations with high index and two classes of $ n $-cycle permutations with low … china running out of moneyWebThe statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations.Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random … grammarly mexico