Results 241 to 250 of about 8,379,944 (285)
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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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Classification of Finite Fields with Applications
Journal of Automated Reasoning, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hing-Lun Chan, Michael Norrish
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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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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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1998
Abstract We shall show in this chapter that for each prime p and positive integer n there is one and only one field with pn elements. This field is sometimes called the Galois field of order pn and is denoted by GF(pn). We shall prove the existence of GF(pn) by showing that there is an irreducible polynomial of degree n over the field
A W Chatters, C R Hajarnavis
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Abstract We shall show in this chapter that for each prime p and positive integer n there is one and only one field with pn elements. This field is sometimes called the Galois field of order pn and is denoted by GF(pn). We shall prove the existence of GF(pn) by showing that there is an irreducible polynomial of degree n over the field
A W Chatters, C R Hajarnavis
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A combined finite element–finite volume framework for phase-field fracture
Computer Methods in Applied Mechanics and Engineering, 2021Inga Berre +2 more
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