New Set of Codes for the Maximum-Likelihood Decoding Problem

The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes. In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A whose decoding bound is beyond the covering radius. For these codes, we show that the maximum-likelihood decoding problem is reachable in polynomial time in the code parameters. Focusing on bi- nary BCH codes, we were able to find several examples of A-covered codes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.Comment: in Yet Another Conference on Cryptography, Porquerolle : France (2010

Re-encoding reformulation and application to Welch-Berlekamp algorithm

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to reduce the practical running time. However, this trick is only devoted for the Koetter interpolation algorithm. We propose a reformulation of the re-encoding for any interpolation methods. The assumption for this reformulation permits only to apply it to the Welch-Berlekamp algorithm

Quantum backflow for many-particle systems

Quantum backflow is the classically-forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of $N$ free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the $N$ identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of $N$.Comment: 12 pages, 2 figure

Application of a Two-Parameter Quantum Algebra to Rotational Spectroscopy of Nuclei

A two-parameter quantum algebra $U_{qp}({\rm u}_2)$ is briefly investigated in this paper. The basic ingredients of a model based on the $U_{qp}({\rm u}_2)$ symmetry, the $qp$-rotator model, are presented in detail. Some general tendencies arising from the application of this model to the description of rotational bands of various atomic nuclei are summarized.Comment: 8 pages, Latex File, to be published in Reports on Mathematical Physic

Water and Economic Growth

Several hydrological studies forecast a global problem of water scarcity. This raises the question as to whether increasing water scarcity may impose constraints on the growth of countries. The influence of water utilization on economic growth is depicted through a growth model that includes this congestible public good as a productive input for private producers. Growth is negatively affected by the government's appropriation of output to supply water but positively influenced by the contribution of increased water use to capital productivity, leading to an inverted-U relationship between economic growth and the rate of water utilization. Crosscountry estimations confirm this relationship and suggest that for most economies current rates of freshwater utilization are not yet constraining growth. However, for a handful of countries, moderate or extreme water scarcity may affect economic growth adversely. Nevertheless, even for water-scarce countries, there appears to be little evidence that there are severe diminishing returns to allocating more output to provide water, thus resulting in falling income per capita. These results suggest caution over the claims of some hydrological-based studies of a widespread global "water crisis".Congestible public goods, cross-country regressions, economic growth, freshwater, water scarcity.

Wet paper codes and the dual distance in steganography

In 1998 Crandall introduced a method based on coding theory to secretly embed a message in a digital support such as an image. Later Fridrich et al. improved this method to minimize the distortion introduced by the embedding; a process called wet paper. However, as previously emphasized in the literature, this method can fail during the embedding step. Here we find sufficient and necessary conditions to guarantee a successful embedding by studying the dual distance of a linear code. Since these results are essentially of combinatorial nature, they can be generalized to systematic codes, a large family containing all linear codes. We also compute the exact number of solutions and point out the relationship between wet paper codes and orthogonal arrays

The variety of reductions for a reductive symmetric pair

We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study these varieties of reductions, and relate the geometry of these variety to some problems in representation theory. A very useful result is the rigidity of semi-simple elements in deformations of algebraic subalgebras of Lie algebras. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.Comment: 23 page

The Joseph ideal for sl(m∣n)\mathfrak{sl}(m|n)

Using deformation theory, Braverman and Joseph obtained an alternative characterisation of the Joseph ideal for simple Lie algebras, which included even type A. In this note we extend that characterisation to define a remarkable quadratic ideal for sl(m|n). When m-n>2 we prove the ideal is primitive and can also be characterised similarly to the construction of the Joseph ideal by Garfinkle

Improving success probability and embedding efficiency in code based steganography

For stegoschemes arising from error correcting codes, embedding depends on a decoding map for the corresponding code. As decoding maps are usually not complete, embedding can fail. We propose a method to ensure or increase the probability of embedding success for these stegoschemes. This method is based on puncturing codes. We show how the use of punctured codes may also increase the embedding efficiency of the obtained stegoschemes