Cumulative-Separable Codes

q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are considered. The relation between different codes from this class is demonstrated. Improved boundaries of the minimum distance and dimension are obtained.Comment: 14 pages, 1 figur

Nonlocal Kinetic Equation and Simulations of Heavy Ion Reactions

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstantaneous scattering integral in the spirit of Enskog corrections is discussed. Numerical values of the off-shell contribution to the Wigner distribution, of the collision duration and of the collision nonlocality are presented for different realistic potentials. On preliminary results we show that simulations of quantum molecular dynamics extended by the nonlocal treatment of collisions leads to a broader proton distribution bringing the theoretical spectra closer towards the experimental values than the local approach.Comment: Proceedings of the Erice School, published as Vol. 42 of "Progress in Particle and Nuclear Physics" by ELSEVIE

SKIRT: the design of a suite of input models for Monte Carlo radiative transfer simulations

The Monte Carlo method is the most popular technique to perform radiative transfer simulations in a general 3D geometry. The algorithms behind and acceleration techniques for Monte Carlo radiative transfer are discussed extensively in the literature, and many different Monte Carlo codes are publicly available. On the contrary, the design of a suite of components that can be used for the distribution of sources and sinks in radiative transfer codes has received very little attention. The availability of such models, with different degrees of complexity, has many benefits. For example, they can serve as toy models to test new physical ingredients, or as parameterised models for inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires algorithms to efficiently generate random positions from 3D density distributions. We describe the design of a flexible suite of components for the Monte Carlo radiative transfer code SKIRT. The design is based on a combination of basic building blocks (which can be either analytical toy models or numerical models defined on grids or a set of particles) and the extensive use of decorators that combine and alter these building blocks to more complex structures. For a number of decorators, e.g. those that add spiral structure or clumpiness, we provide a detailed description of the algorithms that can be used to generate random positions. Advantages of this decorator-based design include code transparency, the avoidance of code duplication, and an increase in code maintainability. Moreover, since decorators can be chained without problems, very complex models can easily be constructed out of simple building blocks. Finally, based on a number of test simulations, we demonstrate that our design using customised random position generators is superior to a simpler design based on a generic black-box random position generator.Comment: 15 pages, 4 figures, accepted for publication in Astronomy and Computin

Redundancy and Aging of Efficient Multidimensional MDS-Parity Protected Distributed Storage Systems

The effect of redundancy on the aging of an efficient Maximum Distance Separable (MDS) parity--protected distributed storage system that consists of multidimensional arrays of storage units is explored. In light of the experimental evidences and survey data, this paper develops generalized expressions for the reliability of array storage systems based on more realistic time to failure distributions such as Weibull. For instance, a distributed disk array system is considered in which the array components are disseminated across the network and are subject to independent failure rates. Based on such, generalized closed form hazard rate expressions are derived. These expressions are extended to estimate the asymptotical reliability behavior of large scale storage networks equipped with MDS parity-based protection. Unlike previous studies, a generic hazard rate function is assumed, a generic MDS code for parity generation is used, and an evaluation of the implications of adjustable redundancy level for an efficient distributed storage system is presented. Results of this study are applicable to any erasure correction code as long as it is accompanied with a suitable structure and an appropriate encoding/decoding algorithm such that the MDS property is maintained.Comment: 11 pages, 6 figures, Accepted for publication in IEEE Transactions on Device and Materials Reliability (TDMR), Nov. 201

Polynomial root finding over local rings and application to error correcting codes

International audienceThis article is devoted to algorithms for computing all the roots of a univariate polynomial with coefficients in a complete commutative Noetherian unramified regular local domain, which are given to a fixed common finite precision. We study the cost of our algorithms, discuss their practical performances, and apply our results to the Guruswami and Sudan list decoding algorithm over Galois rings