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We propose a systematic method to produce potentially good recursive towers over finite fields. The graph point of view, so as some magma and sage computations are used in this process. We also establish some theoretical functional criterion ensuring the existence of many rational points on a recursive tower. Both points are illustrated by an example, from the production process, to the theoretical study. 相似文献
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For any positive integers and , we prove that the number of monic irreducible polynomials of degree n over in which the coefficients of , and are prescribed has period 24 as a function of n, after a suitable normalization. A similar result holds over , with the period being 60. We also show that this is a phenomena unique to characteristics 2 and 5. The result is strongly related to the supersingularity of certain curves associated with cyclotomic function fields, and in particular it complements an equidistribution result of Katz. 相似文献
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Stphane Ballet 《Finite Fields and Their Applications》2003,9(4):472
From the existence of a tower of algebraic function fields with more steps than the Garcia–Stichtenoth tower, we improve upper bounds on the bilinear complexity of multiplication in all extensions of the finite field
where q is an arbitrary prime power. 相似文献
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In this paper, we completely determine all necessary and sufficient conditions such that the polynomial , where , is a permutation quadrinomial of over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where and finally, in [16], Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial , where and and proposed some new classes of permutation quadrinomials of .In particular, in this paper we classify all permutation polynomials of of the form , where , over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. 相似文献
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Every elliptic quartic Γ4 of PG(3,q) with nGF(q)-rational points provides a near-MDS code C of length n and dimension 4 such that the collineation group of Γ4 is isomorphic to the automorphism group of C. In this paper we assume that GF(q) has characteristic p>3. We classify the linear collineation groups of PG(3,q) which can preserve an elliptic quartic of PG(3,q). Also, we prove for q?113 that if the j-invariant of Γ4 does not disappear, then C cannot be extended in a natural way by adding a point of PG(3,q) to Γ4. 相似文献
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Cemile Tosun 《Discrete Mathematics》2019,342(12):111618
In this paper, we derive explicit factorizations of generalized cyclotomic polynomials and generalized Dickson polynomials of the first kind of order , over finite field . 相似文献
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Satoh's algorithm in characteristic 2 总被引:3,自引:0,他引:3
Berit Skjernaa. 《Mathematics of Computation》2003,72(241):477-487
We give an algorithm for counting points on arbitrary ordinary elliptic curves over finite fields of characteristic , extending the method given by Takakazu Satoh, giving the asymptotically fastest point counting algorithm known to date.
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In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in
, the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in
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