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Permutations in a Finite Field [PDF]
Proceedings of the American Mathematical Society, 1953 (1) ax + f, xQ-2 (at: EGF(q), a # 0). For q = 5, this was proved to be true by Betti; for q =7 the corresponding result was verified by Dickson [1, p. 119]. In this note we show very simply that this result holds for all q. Since the totality of permutation polynomials evidently furnishes a representation of the symmetric group on q letters, it will ...
L. Carlitz
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An adaptive cryptosystem on a Finite Field. [PDF]
PeerJ Comput Sci, 2021 Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information. This paper introduces an adaptive block encryption scheme.
Bhowmik A, Menon U.
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Computation with finite fields
Information and Control, 1963 A technique for systematically generating representations of finite fields is presented. Relations which must be physically realized in order to implement a parallel arithmetic unit to add, multiply, and divide elements of finite fields of 2n elements are obtained.
Thomas C. Bartee, David Schneider
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Finite Fourier series and equations in finite fields [PDF]
Transactions of the American Mathematical Society, 1953 Albert Leon Whiteman
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A theorem about linear rank inequalities that depend on the characteristic of the finite field
Selecciones Matemáticas, 2022 A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over ...
Victor Peña-Macias
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Barekeng, 2021 Kode blok adalah skema penyandian yang menggunakan sistem kode-kode pada suatu lapangan hingga dengan panjang yang sama dan tetap. Kode blok linear atau lebih sering disebut kode linear atas suatu lapangan hingga merupakan himpunan kode-kode blok dengan ...
Juli Loisiana Butar-Butar +1 more
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On the number of irreducible polynomials of special kinds in finite fields
AIMS Mathematics, 2020 Let $\mathbb{F}_q$ be the finite field of order $q$ and $f(x)$ be an irreducible polynomial of degree $n$ over $\mathbb{F} _q$. For a positive divisor $n_1$ of $n$, define the $n_1$-traces of $f(x)$ to be $\mathrm{Tr}(\alpha;n_1)=\alpha+\alpha^q+\cdots ...
Weihua Li, Chengcheng Fang, Wei Cao
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Counting Quiver Representations over Finite Fields Via Graph Enumeration [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $\Gamma$ be a quiver on $n$ vertices $v_1, v_2, \ldots , v_n$ with $g_{ij}$ edges between $v_i$ and $v_j$, and let $\boldsymbol{\alpha} \in \mathbb{N}^n$.
Geir Helleloid +1 more
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The number of rational points of certain quartic diagonal hypersurfaces over finite fields
AIMS Mathematics, 2020 Let $p$ be an odd prime and let $\mathbb{F}_q$ be a finite field of characteristic $p$ with order $q=p^s$. For $f(x_1, \cdots, x_n)\in\mathbb{F}_q[x_1, ..., x_n]$, we denote by $N(f(x_1, \cdots, x_n)=0)$ the number of $\mathbb{F}_q$-rational points on ...
Junyong Zhao, Shaofang Hong, Chaoxi Zhu
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