205 research outputs found
Asymptotic Bound on Binary Self-Orthogonal Codes
We present two constructions for binary self-orthogonal codes. It turns out
that our constructions yield a constructive bound on binary self-orthogonal
codes. In particular, when the information rate R=1/2, by our constructive
lower bound, the relative minimum distance \delta\approx 0.0595 (for GV bound,
\delta\approx 0.110). Moreover, we have proved that the binary self-orthogonal
codes asymptotically achieve the Gilbert-Varshamov bound.Comment: 4 pages 1 figur
On the Density of Coprime m-tuples over Holomorphy Rings
Let be a finite field, be a function field of
genus having full constant field , a set of
places of and the holomorphy ring of . In this paper we
compute the density of coprime -tuples of elements of . As a side result,
we obtain that whenever the complement of is finite, the
computation of the density can be reduced to the computation of the
-polynomial of the function field. In the rational function field case,
classical results for the density of coprime -tuples of polynomials are
obtained as corollaries.Comment: To appear in International Journal of Number Theor
On the Invariants of Towers of Function Fields over Finite Fields
We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field
F_q and a finite extension E/F_0 such that the sequence
\mathcal{E):=(EF_n)_{n\goq 0} is a tower over the field F_q. Then we deal with
the following: What can we say about the invariants of \mathcal{E}; i.e., the
asymptotic number of places of degree r for any r\geq 1 in \mathcal{E}, if
those of F are known? We give a method based on explicit extensions for
constructing towers of function fields over F_q with finitely many prescribed
invariants being positive, and towers of function fields over F_q, for q a
square, with at least one positive invariant and certain prescribed invariants
being zero. We show the existence of recursive towers attaining the
Drinfeld-Vladut bound of order r, for any r\geq 1 with q^r a square. Moreover,
we give some examples of recursive towers with all but one invariants equal to
zero.Comment: 23 page
On the Value Set of n! Modulo a Prime
This is a preprint of an article published by TĂBÄ°TAK; William D. Banks, Florian Luca, Igor E. Shparlinski, Henning Stichtenoth, âOn the value set of n! modulo a prime,â Turkish Journal of Mathematics, 29 (2005), 169-174. Copyright ©2005.We show that for infinitely many prime numbers p there are at least log log p/ log log log p distinct residue classes modulo p that are not congruent to n! for any integer n
On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields
International audienceWe indicate a strategy in order to construct bilinear multiplication algorithms of type Chudnovsky in large extensions of any finite field. In particular, using the symmetric version of the generalization of Randriambololona specialized on the elliptic curves, we show that it is possible to construct such algorithms with low bilinear complexity. More precisely, if we only consider the Chudnovsky-type algorithms of type symmetric elliptic, we show that the symmetric bilinear complexity of these algorithms is in O(n(2q)^log * q (n)) where n corresponds to the extension degree, and log * q (n) is the iterated logarithm. Moreover, we show that the construction of such algorithms can be done in time polynomial in n. Finally, applying this method we present the effective construction, step by step, of such an algorithm of multiplication in the finite field F 3^57. Index Terms Multiplication algorithm, bilinear complexity, elliptic function field, interpolation on algebraic curve, finite field
Efficient Doubling on Genus Two Curves over Binary Fields
In most algorithms involving elliptic and hyperelliptic curves, the costliest part consists in computing multiples of ideal classes. This paper investigates how to compute faster doubling over fields of characteristic two.
We derive explicit doubling formulae making strong use of the defining equation of the curve. We analyze how many field operations are needed depending on the curve making clear how much generality one loses by the respective choices. Note, that none of the proposed types is known to
be weak â one only could be suspicious because of the more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only half the time of an addition. Combined with a sliding window method this leads to fast computation
of scalar multiples. We also speed up the general case
On rationality of the intersection points of a line with a plane quartic
We study the rationality of the intersection points of certain lines and
smooth plane quartics C defined over F_q. For q \geq 127, we prove the
existence of a line such that the intersection points with C are all rational.
Using another approach, we further prove the existence of a tangent line with
the same property as soon as the characteristic of F_q is different from 2 and
q \geq 66^2+1. Finally, we study the probability of the existence of a rational
flex on C and exhibit a curious behavior when the characteristic of F_q is
equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case;
Conjecture 1 from the previous version is proved wron
Effect of Cyclooxygenase(COX)-1 and COX-2 inhibition on furosemide-induced renal responses and isoform immunolocalization in the healthy cat kidney
BACKGROUND: The role of cyclooxygenase(COX)-1 and COX-2 in the saluretic and renin-angiotensin responses to loop diuretics in the cat is unknown. We propose in vivo characterisation of isoform roles in a furosemide model by administering non-steroidal anti-inflammatory drugs (NSAIDs) with differing selectivity profiles: robenacoxib (COX-2 selective) and ketoprofen (COX-1 selective). RESULTS: In this four period crossover study, we compared the effect of four treatments: placebo, robenacoxib once or twice daily and ketoprofen once daily concomitantly with furosemide in seven healthy cats. For each period, urine and blood samples were collected at baseline and within 48 h of treatment starting. Plasma renin activity (PRA), plasma and urinary aldosterone concentrations, glomerular filtration rate (GFR) and 24 h urinary volumes, electrolytes and eicosanoids (PGE(2), 6-keto-PGF1(α,) TxB(2)), renal injury biomarker excretions [N-acetyl-beta-D-glucosaminidase (NAG) and Gamma-Glutamyltransferase] were measured. Urine volume (24 h) and urinary sodium, chloride and calcium excretions increased from baseline with all treatments. Plasma creatinine increased with all treatments except placebo, whereas GFR was significantly decreased from baseline only with ketoprofen. PRA increased significantly with placebo and once daily robenacoxib and the increase was significantly higher with placebo compared to ketoprofen (10.5â±â4.4 vs 4.9â±â5.0 ng ml(â1) h(â1)). Urinary aldosterone excretion increased with all treatments but this increase was inhibited by 75 % with ketoprofen and 65 % with once daily robenacoxib compared to placebo. Urinary PGE(2) excretion decreased with all treatments and excretion was significantly lower with ketoprofen compared to placebo. Urinary TxB(2) excretion was significantly increased from baseline only with placebo. NAG increased from baseline with all treatments. Immunohistochemistry on post-mortem renal specimens, obtained from a different group of cats that died naturally of non-renal causes, suggested constitutive COX-1 and COX-2 co-localization in many renal structures including the macula densa (MD). CONCLUSIONS: These data suggest that both COX-1 and COX-2 could generate the signal from the MD to the renin secreting cells in cats exposed to furosemide. Co-localization of COX isoenzymes in MD cells supports the functional data reported here. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12917-015-0598-z) contains supplementary material, which is available to authorized users
On lattice profile of the elliptic curve linear congruential generators
Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of BrandstÀtter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG
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