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 $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-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 TÜBİTAK; William D. Banks, Florian Luca, Igor E. Shparlinski, Henning Stichtenoth, “On the value set of n! modulo a prime,” 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

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 – 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 (10.5 ± 4.4 vs 4.9 ± 5.0 ng ml(−1) h(−1)). 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 Brandstätter 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

On the complexity of arithmetic secret sharing

Since the mid 2000s, asymptotically-good strongly-multiplicative linear (ramp) secret sharing schemes over a fixed finite field have turned out as a central theoretical primitive in numerous constant-communication-rate results in multi-party cryptographic scenarios, and, surprisingly, in two-party cryptography as well. Known constructions of this most powerful class of arithmetic secret sharing schemes all rely heavily on algebraic geometry (AG), i.e., on dedicated AG codes based on asymptotically good towers of algebraic function fields defined over finite fields. It is a well-known open question since the first (explicit) constructions of such schemes appeared in CRYPTO 2006 whether the use of “heavy machinery” can be avoided here. i.e., the question is whether the mere existence of such schemes can also be proved by “elementary” techniques only (say, from classical algebraic coding theory), even disregarding effective construction. So far, there is no progress. In this paper we show the theoretical result that, (1) no matter whether this open question has an affirmative answer or not, these schemes can be constructed explicitly by elementary algorithms defined in terms of basic algebraic coding theory. This pertains to all relevant operations associated to such schemes, including, notably, the generation of an instance for a given number of players n, as well as error correction in the presence of corrupt shares. We further show that (2) the algorithms are quasi-linear time (in n); this is (asymptotically) significantly more efficient than the known constructions. That said, the analysis of the mere termination of these algorithms does still rely on algebraic geometry, in the sense that it requires “blackbox application” of suitable existence results for these schemes. Our method employs a nontrivial, novel adaptation of a classical (and ubiquitous) paradigm from coding theory that enables transformation of existence results on asymptotically good codes into explicit construction of such codes via concatenation, at some constant loss in parameters achieved. In a nutshell, our generating idea is to combine a cascade of explicit but “asymptotically-bad-yet-good-enough schemes” with an asymptotically good one in such a judicious way that the latter can be selected with exponentially small number of players in that of the compound scheme. This opens the door t