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An extension of binary cyclotomic sequences having order 2lt
Discrete Mathematics, Algorithms and Applications, 2022Several reasonably cyclotomic sequences are constructed by cyclotomic classes having good pseudo-randomness property. In this paper, we derive the linear complexity of an extended binary cyclotomic sequences of order [Formula: see text] over finite field having period [Formula: see text].
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2001
In this chapter we shall describe the work of Gauss and Lagrange on the resolution by radicals of cyclotomic polynomials. Then we will describe some of the work of Jacobi and Kummer on the ideal theory of rings of cyclotomic integers.
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In this chapter we shall describe the work of Gauss and Lagrange on the resolution by radicals of cyclotomic polynomials. Then we will describe some of the work of Jacobi and Kummer on the ideal theory of rings of cyclotomic integers.
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ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
Mathematics of the USSR-Izvestiya, 1980This paper is devoted to the realization of certain types of Chevalley groups as the Galois group of extensions of certain cyclotomic fields. In addition, a criterion for an algebraic curve to be defined over an algebraic number field is given. Bibliography: 11 titles.
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Kummer Theory over Cyclotomic Zp-extensions
1978In the last chapter we studied the ideal class groups in a Z p -extension of a number field. Here we shall consider especially the cyclotomic Z p -extension, and then Kummer extensions above it, as in Iwasawa [Iw 12], obtained by adjoining p n th roots of units, p-units, and ideal classes of p-power order.
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Normal bases for quadratic extensions inside cyclotomic fields
Archiv der Mathematik, 1996Let \(L= \mathbb{Q}[\zeta_p]\) be the cyclotomic extension, \(p\) a prime, and let \(\mathbb{Q}\subset F\subset E\subset L\) with \(E/F\) a quadratic extension. The author constructs an explicit normal basis of \({\mathcal O}_E\) over \({\mathcal O}_F\).
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A primality test using cyclotomic extensions
1989The cyclotomic polynomial Φs(x) (where s is an integer >1) is the irreducible polynomial over ℚ, having the primitive s-th roots of unity as zeroes. If \(\mathbb{K}\) is the field ℚ or \(\mathbb{F}_p\), with p a prime, an s-th cyclotomic extension of \(\mathbb{K}\) is the splitting field of Φs(x) over \(\mathbb{K}\).
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ON ABELIAN EXTENSIONS OVER CYCLOTOMIC ZPl × ... × ZPt-EXTENSIONS
Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics, 1984openaire +1 more source