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Classification of Finite Fields with Applications
Journal of Automated Reasoning, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hing-Lun Chan, Michael Norrish
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52nd IEEE Conference on Decision and Control, 2013
This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers {0,..., p-1}, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence ...
Fabio Pasqualetti +2 more
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This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers {0,..., p-1}, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence ...
Fabio Pasqualetti +2 more
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On involutions of finite fields
2015 IEEE International Symposium on Information Theory (ISIT), 2015In this paper we study involutions over a finite field of order $\bf 2^n$. We present some classes, several constructions of involutions andwe study the set of their fixed points.
Charpin, Pascale +2 more
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1981 IEEE 5th Symposium on Computer Arithmetic (ARITH), 1981
The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field GF(2m) are implemented as polynomial operations using binary logic of flip-flops and EXOR's.
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The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field GF(2m) are implemented as polynomial operations using binary logic of flip-flops and EXOR's.
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Information Processing Letters, 1982
Let \(p\) be a fixed prime and \(n=m_1m_2\cdots m_l\) be a factorization of a positive integer \(n\) such that \(m_1\ge m_2\ge \ldots\ge m_l\ge 1\). The author proposes an algorithm for realizing the finite field \(\mathrm{GF}(p^n)\) with \(p^n\) elements, by the chain of field extensions \[ \mathrm{GF}(p)\subseteq \mathrm{GF}(p^{m_1})\subseteq \mathrm{
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Let \(p\) be a fixed prime and \(n=m_1m_2\cdots m_l\) be a factorization of a positive integer \(n\) such that \(m_1\ge m_2\ge \ldots\ge m_l\ge 1\). The author proposes an algorithm for realizing the finite field \(\mathrm{GF}(p^n)\) with \(p^n\) elements, by the chain of field extensions \[ \mathrm{GF}(p)\subseteq \mathrm{GF}(p^{m_1})\subseteq \mathrm{
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On the finite field Nullstellensatz
Australas. J Comb., 2000Let \(\mathbb{P}^n\) be the \(n\)-dimensional projective space defined over an algebraically closed field of positive characteristic \(p\), let \(q\) be a power of \(p\) and let \(X\) be an irreducible closed \(\mathbb{F}_q\)-definable subvariety of \(\mathbb{P}^n\) (here \(\mathbb{F}_q\) denotes the Galois field of \(q\) elements).
E. BALLICO, COSSIDENTE, Antonio
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A Sárközy Theorem for Finite Fields
Combinatorics, Probability and Computing, 2003A classical result of Sárközy states that, for any and any positive density subset E of , there exist elements x and y of E and such that . A version of this result for finite fields is derived from a recent theorem of P. Larick, a short proof of which is also given.
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Unknown finite fields as to the boolean finite fields theory
Journal of Discrete Mathematical Sciences and Cryptography, 2014AbstractThis note presents a canonical construction of the structures of modal Θ -valent field ( mΘf) and modal Θ -valent pseudo field (mΘpf) as defined by F. Ayissi Eteme in (9). Their respective sets of the invertibles and modal Θ -invertibles are modal Θ -valent groups ( mΘg).
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Synchronous Networks Over Finite Fields
IEEE Transactions on Automatic Control, 2023Hua-Lin Huang, Jin Wang, Yongyuan Yu
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Synchronization of Networks Over Finite Fields
Automatica, 2020Gaoxi Xiao, Xiuxian Li, Min Meng
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