2,077 research outputs found
Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary
code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1)
where V(n,d) stands for the volume of a Hamming ball of radius d. Recently
Jiang and Vardy showed that for binary non-linear codes this bound can be
improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In
this paper we show that certain asymptotic families of linear binary [n,n/2]
random double circulant codes satisfy the same improved Gilbert-Varshamov
bound.Comment: Submitted to IEEE Transactions on Information Theor
On the construction of dense lattices with a given automorphism group
We consider the problem of constructing dense lattices of R^n with a given
automorphism group. We exhibit a family of such lattices of density at least
cn/2^n, which matches, up to a multiplicative constant, the best known density
of a lattice packing. For an infinite sequence of dimensions n, we exhibit a
finite set of lattices that come with an automorphism group of size n, and a
constant proportion of which achieves the aforementioned lower bound on the
largest packing density. The algorithmic complexity for exhibiting a basis of
such a lattice is of order exp(nlogn), which improves upon previous theorems
that yield an equivalent lattice packing density. The method developed here
involves applying Leech and Sloane's construction A to a special class of codes
with a given automorphism group, namely the class of double circulant codes.Comment: 10 pages. Corrected typos and ambiguous definitio
Polynomial-Time Key Recovery Attack on the Faure-Loidreau Scheme based on Gabidulin Codes
Encryption schemes based on the rank metric lead to small public key sizes of
order of few thousands bytes which represents a very attractive feature
compared to Hamming metric-based encryption schemes where public key sizes are
of order of hundreds of thousands bytes even with additional structures like
the cyclicity. The main tool for building public key encryption schemes in rank
metric is the McEliece encryption setting used with the family of Gabidulin
codes. Since the original scheme proposed in 1991 by Gabidulin, Paramonov and
Tretjakov, many systems have been proposed based on different masking
techniques for Gabidulin codes. Nevertheless, over the years all these systems
were attacked essentially by the use of an attack proposed by Overbeck.
In 2005 Faure and Loidreau designed a rank-metric encryption scheme which was
not in the McEliece setting. The scheme is very efficient, with small public
keys of size a few kiloBytes and with security closely related to the
linearized polynomial reconstruction problem which corresponds to the decoding
problem of Gabidulin codes. The structure of the scheme differs considerably
from the classical McEliece setting and until our work, the scheme had never
been attacked. We show in this article that this scheme like other schemes
based on Gabidulin codes, is also vulnerable to a polynomial-time attack that
recovers the private key by applying Overbeck's attack on an appropriate public
code. As an example we break concrete proposed bits security parameters in
a few seconds.Comment: To appear in Designs, Codes and Cryptography Journa
A new class of codes for Boolean masking of cryptographic computations
We introduce a new class of rate one-half binary codes: {\bf complementary
information set codes.} A binary linear code of length and dimension
is called a complementary information set code (CIS code for short) if it has
two disjoint information sets. This class of codes contains self-dual codes as
a subclass. It is connected to graph correlation immune Boolean functions of
use in the security of hardware implementations of cryptographic primitives.
Such codes permit to improve the cost of masking cryptographic algorithms
against side channel attacks. In this paper we investigate this new class of
codes: we give optimal or best known CIS codes of length We derive
general constructions based on cyclic codes and on double circulant codes. We
derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all
be classified in small lengths by the building up construction. Some
nonlinear permutations are constructed by using -codes, based on the
notion of dual distance of an unrestricted code.Comment: 19 pages. IEEE Trans. on Information Theory, to appea
Disaggregation of global ensemble rainfall forecasts for improved stormwater management
Les bassins de rĂ©tention sans plan d'eau permanent (bassins "secs") sont largement rĂ©pandus pour diminuer les aspects nĂ©gatifs du ruissellement urbain sur le milieu rĂ©cepteur. Ă l'heure actuelle, de tels bassins sont conçus avec un contrĂŽle statique, ce qui signifie que leur fonctionnement est seulement basĂ© sur une limitation de leur dĂ©bit maximal de sortie. Le ContrĂŽle en Temps RĂ©el (CTR) du degrĂ© d'ouverture de leur vanne de sortie permettrait d'amĂ©liorer leurs performances. Le travail prĂ©sentĂ© ici a notamment permis le dĂ©veloppement de scĂ©narios de CTR d'un bassin de rĂ©tention sec situĂ© Ă l'exutoire d'une petite zone urbaine (3.5 km2) sur le territoire de la Ville de QuĂ©bec, au Canada. Le ruissellement et sa concentration en MatiĂšres En Suspension (MES) ont Ă©tĂ© simulĂ©s par le modĂšle SWMM5, dans lequel la formulation du lessivage de surface a Ă©tĂ© amĂ©liorĂ©e dans le cadre de ce travail. Les stratĂ©gies de gestion en temps rĂ©el proposĂ©es utilisent comme information les donnĂ©es du rĂ©seau pluviomĂ©trique, la mesure de la hauteur d'eau dans le bassin de rĂ©tention et, dans certains des scĂ©narios, des prĂ©visions mĂ©tĂ©orologiques. Les prĂ©visions de pluie peuvent en effet s'avĂ©rer intĂ©ressantes pour une large gamme d'utilisateurs, comme ceux impliquĂ©s dans la prĂ©vention des crues, et la gestion de l'eau de maniĂšre gĂ©nĂ©rale, puisqu'elles permettent une certaine anticipation du comportement du systĂšme. Les prĂ©visions de pluie d'ensemble fournissent de plus une description explicite et dynamique de l'incertitude liĂ©e Ă la prĂ©vision. Cependant, de telles prĂ©visions sont Ă l'heure actuelle disponibles Ă des Ă©chelles trop grandes pour ĂȘtre directement compatibles avec des modĂšles hydrologiques mis en Ćuvre sur de petits bassins versants. Cette thĂšse de doctorat s'est donc de plus penchĂ©e sur la dĂ©sagrĂ©gation spatiale du systĂšme de prĂ©vision d'ensemble Canadien, afin de rendre les prĂ©visions d'ensemble de pluie plus appropriĂ©es Ă l'Ă©chelle du petit bassin urbain pour lequel des rĂšgles de CTR du bassin de rĂ©tention ont Ă©tĂ© Ă©laborĂ©es. Pour cela, diverses variantes de la mĂ©thode statistique de dĂ©sagrĂ©gation spatiale proposĂ©e par Perica et Foufoula-Georgiou (1996b) ont Ă©tĂ© comparĂ©es, pour faire passer les prĂ©visions d'ensemble globales de pluie (Ă©mises par Environnement Canada) d'une rĂ©solution de 100 km par 70 km Ă celle de 6 km par 4 km. Cette technique permet d'augmenter la variance des hauteurs de pluie prĂ©vues Ă l'intĂ©rieur d'un pixel original lors de la dĂ©sagrĂ©gation, tout en prĂ©servant la valeur moyenne initialement prĂ©vue pour la pluie sur ce pixel. Ces prĂ©visions d'ensemble de pluie ont Ă©tĂ© Ă©mises par le systĂšme de prĂ©vision d'ensemble global Canadien, dans sa forme opĂ©rationnelle en 2009. La mĂ©thode statistique de Skaugen (2002) a Ă©galement Ă©tĂ© appliquĂ©e Ă ces prĂ©visions, et a menĂ© Ă la production de prĂ©visions d'ensemble ayant une rĂ©solution de 10 km par 7 km. Pour comparaison, des mĂ©thodes plus simples comme celle de l'interpolation bilinĂ©aire, ont aussi Ă©tĂ© appliquĂ©es. Cette derniĂšre permet le raffinement des prĂ©visions globales de pluie sans augmenter la variance des hauteurs de pluie lors du processus de raffinement spatial. Les produits mĂ©tĂ©orologiques dĂ©sagrĂ©gĂ©s ont Ă©tĂ© Ă©valuĂ©s d'un point de vue mĂ©tĂ©orologique et hydrologique, en utilisant diffĂ©rents scores et diagrammes. Pour l'Ă©valuation mĂ©tĂ©orologique, neuf jours prĂ©sentant d'importants Ă©vĂšnements de prĂ©cipitation ont Ă©tĂ© utilisĂ©s pour comparer les hauteurs de pluie prĂ©vues Ă celles observĂ©es par le rĂ©seau de pluviomĂštres de la ville de QuĂ©bec. Des prĂ©visions hydrologiques d'ensemble avec un pas de temps compris entre 3 et 24 heures ont Ă©tĂ© mises en Ćuvre sur une pĂ©riode de 3 mois, avec les prĂ©visions d'ensemble originales et celles issues de la dĂ©sagrĂ©gation. Cette chaĂźne de prĂ©vision hydro-mĂ©tĂ©orologique opĂ©rationnelle a Ă©tĂ© Ă©laborĂ©e en utilisant les modĂšles GR4J et SWMM5. Ces modĂšles ont Ă©tĂ© mis en Ćuvre sur 4 bassins situĂ©s dans la rĂ©gion de QuĂ©bec, avec une taille comprise entre 5 et 350 km2. L'Ă©valuation hydrologique s'est basĂ©e sur la comparaison des dĂ©bits prĂ©vus avec ceux observĂ©s. Les rĂ©sultats obtenus avec la mĂ©thode de Skaugen (2002) ne se sont pas rĂ©vĂ©lĂ©s aussi intĂ©ressants que ceux basĂ©s sur la technique de Perica et Foufoula-Georgiou (1996b). Avec cette derniĂšre, les conclusions principales de ce travail de thĂšse sont: 1) la qualitĂ© globale des prĂ©visions est prĂ©servĂ©e lors du processus de raffinement, et 2) les produits dĂ©sagrĂ©gĂ©s par cette mĂ©thode qui permet d'augmenter la variance des hauteurs de pluie prĂ©sentent une qualitĂ© similaire Ă celle des produits dĂ©sagrĂ©gĂ©s par la mĂ©thode de l'interpolation bilinĂ©aire. En revanche, la variance et la dispersion des diffĂ©rents membres des prĂ©visions d'ensemble se sont avĂ©rĂ©es largement amĂ©liorĂ©es pour les produits dĂ©sagrĂ©gĂ©s par la mĂ©thode de Perica et Foufoula-Georgiou (1996b), ce qui reprĂ©sente un avantage considĂ©rable comparativement Ă la mĂ©thode de l'interpolation bilinĂ©aire. Ces rĂ©sultats ont Ă©tĂ© confirmĂ©s du point de vue hydrologique. Par consĂ©quent, il est avancĂ© Ă l'issue de ces travaux de doctorat que la mĂ©thode de dĂ©sagrĂ©gation statistique de Perica and Foufoula-Georgiou (1996b) reprĂ©sente une maniĂšre intĂ©ressante pour rĂ©duire le problĂšme d'incompatibilitĂ© existant entre les rĂ©solutions des modĂšles mĂ©tĂ©orologiques globaux et le haut degrĂ© de prĂ©cision parfois requis dans la reprĂ©sentation spatiale des champs de prĂ©cipitation par les modĂšles hydrologiques semi-distribuĂ©s et par ceux montĂ©s sur de petits bassins versants. Les stratĂ©gies de CTR mises en place pour le bassin de rĂ©tention sec Ă©tudiĂ© ici ont permis une amĂ©lioration significative de ses performances - l'efficacitĂ© d'enlĂšvement des MES est passĂ©e de 46 Ă 90% - tout en restant sĂ©curitaire (du point de vue du risque de dĂ©bordement) et en prenant en compte une contrainte liĂ©e au risque de prolifĂ©ration de moustiques. Cependant, les prĂ©visions de pluie dĂ©sagrĂ©gĂ©es ne se sont pas rĂ©vĂ©lĂ©es supĂ©rieures aux prĂ©visions originales du modĂšle d'ensemble global Canadien, dans ce contexte spĂ©cifique de gestion en temps rĂ©el. Les diffĂ©rentes prĂ©visions considĂ©rĂ©es ont en effet menĂ© Ă des rĂ©sultats similaires pour les performances de ce bassin de rĂ©tention soumis Ă des rĂšgles de CTR. Dry detention ponds are commonly implemented to mitigate the impacts of urban runoff on receiving water bodies. They currently rely on static control through a fixed limitation of their maximum outflow rate. Real-Time Control (RTC) allows optimizing their performance by manipulation of an outlet valve. This thesis developed several enhanced RTC scenarios of a dry detention pond located at the outlet of a small (3.5 km2) urban catchment near QuĂ©bec City, Canada. The catchment's runoff quantity and Total Suspended Solids' (TSS) concentration were simulated by the SWMM5 model with an improved wash-off formulation. The control procedures rely on rain gauge data, on measures of the pond's water height, and, in some of the RTC scenarios, on rainfall forecasts. Rainfall forecasts are indeed valuable to a wide variety of end users in the field of flood risk assessment and water management, as they allow some anticipation of the behaviour of the system under consideration. Ensemble rainfall forecasts thus provide an explicit and dynamic assessment of the uncertainty in the forecast. However, for hydrological forecasting, their low resolution currently limits their use to large watersheds. Therefore, this thesis explores rendering the Canadian Ensemble Prediction System's (EPS's) rainfall forecasts more appropriate for hydrological modeling of such a small urban catchment as the one studied here. To bridge this spatial gap, various implementations of the spatial statistical downscaling method proposed by Perica and Foufoula-Georgiou (1996b) were compared, bringing Environment Canada's (EC's) global Ensemble Rainfall Forecasts (ERFs) from a 100-km by 70-km resolution down to 6-km by 4-km, while increasing each pixel's rainfall variance and preserving its original mean. These ERFs were issued by the Canadian Global Ensemble Prediction System (GEPS) in its 2009 operational version. The statistical downscaling method of Skaugen (2002) was also applied to these ERFs, producing rainfall fields with a resolution of 10 km by 7 km. For comparison purposes, simpler methods were also implemented such as the bi-linear interpolation, which disaggregates global forecasts without modifying their variance. The downscaled meteorological products were evaluated, using different scores and diagrams, from both a meteorological and a hydrological view points. The rainfall forecasts were compared against nine days (presenting strong precipitation events) of observed values taken from QuĂ©bec City's rain gauge database. Ensemble Hydrologic Forecasts (EHFs) with a time step of 3 and 24 hours were performed over a 3-month period for the original and disaggregated rainfall forecasts. This hydro-meteorological operational forecasting chain was conducted using hydrological models GR4J, a modified version of GR4J, and SWMM5. These models were implemented on four catchments ranging between 5 and 350 km2, and located in the QuĂ©bec City region. The hydrological evaluation was based on the comparison of forecasted flows to the observed ones. Results obtained with the method of Skaugen (2002) were not as interesting as those based on the technique of Perica and Foufoula-Georgiou (1996b). This is due to the fact that with the method of Skaugen (2002), the final rainfall field corresponds to the average of ten downscaled fields, what tends to dampen the variance added through the disaggregation process. For the technique of Perica and Foufoula-Georgiou (1996b), the most important conclusions are: 1) the overall quality of the forecasts is preserved during the disaggregation procedure and 2) the disaggregated products using the variance-enhancing method are of similar quality than bi-linear interpolation products. However, variance and dispersion of the different members are, of course, much improved for the variance-enhanced products, compared to the bi-linear interpolation, which is a decisive advantage. These results were confirmed by the hydrological evaluation. The disaggregation technique of Perica and Foufoula-Georgiou (1996b) hence represents an interesting way of bridging the gap between the resolution of meteorological models and the high degree of spatial precision sometimes required (in the precipitation representation) by semi-distributed hydrological models and by models built on small watersheds. RTC strategies of the studied dry pond allowed for a substantial improvement of the performance compared to those with its current static controlâ the TSS removal efficiency increased from 46 to about 90% - while remaining safe and taking a mosquito-breeding risk constraint into account. However, the downscaled rainfall forecasts were not superior to the original ones (issued by the Canadian GEPS) in this context, as they led to the same performance for the RTC scenarios relying on rainfall forecasts.

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