The Dimension of Subcode-Subfields of Shortened Generalized Reed Solomon Codes

Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is static, the appropriate length can be obtained by an RS code by shortening or puncturing. Generalized Reed-Solomon (GRS) codes are a generalization of RS codes, whose subfield-subcodes are extensively studied. In this paper we show that a particular class of GRS codes produces many subfield-subcodes with large dimension. An algorithm for searching through the codes is presented as well as a list of new codes obtained from this method

Subfield-Subcodes of Generalized Toric codes

We study subfield-subcodes of Generalized Toric (GT) codes over $\mathbb{F}_{p^s}$. These are the multidimensional analogues of BCH codes, which may be seen as subfield-subcodes of generalized Reed-Solomon codes. We identify polynomial generators for subfield-subcodes of GT codes which allows us to determine the dimensions and obtain bounds for the minimum distance. We give several examples of binary and ternary subfield-subcodes of GT codes that are the best known codes of a given dimension and length.Comment: Submitted to 2010 IEEE International Symposium on Information Theory (ISIT 2010

Effect of the hard magnetic inclusion on the macroscopic anisotropy of nanocrystalline magnetic-materials

It is shown that the presence of highly anisotropic magnetic precipitates in a soft multiphased matrix can produce a remarkable hardening, even when the volume fraction of the precipitates is small. The exchange coupling between the matrix and the precipitates is the relevant parameter. In particular, the simplified analysis we develop in this paper accounts for the magnetic hardening observed in very soft Fe-rich nanocrystals after annealing at higher temperatures

Universal angular magnetoresistance and spin torque in ferromagnetic/normal metal hybrids

The electrical resistance of ferromagnetic/normal-metal (F/N) heterostructures depends on the nature of the junctions which may be tunnel barriers, point contacts, or intermetallic interfaces. For all junction types, the resistance of disordered F/N/F perpendicular spin valves as a function of the angle between magnetization vectors is shown to obey a simple universal law. The spin-current induced magnetization torque can be measured by the angular magnetoresistance of these spin valves. The results are generalized to arbitrary magnetoelectronic circuits

From Digital to Analogue Magnetoelectronics: Theory of Transport in Non-Collinear Magnetic Nanostructures

Magnetoelectronics is mainly digital, i.e. governed by up and down magnetizations. In contrast, analogue magnetoelectronics makes use of phenomena occuring for non-collinear magnetization configurations. Here we review theories which have recently been applied to the transport in non-collinear magnetic nanostructures in two and multiterminal structures, viz. random matrix and circuit theory. Both are not valid for highly transparent systems in a resistive environment like perpendicular metallic spin valves. The solution to this problem is a renormalization of the conventional and spin-mixing conductance parameters.Comment: To be published in "Advance in Solid State Physics", edited by B. Kramer, Springer Verlag, Berlin, 200

Tracking Event Model

This note presents the LHCb Tracking Event Model. It discusses the requirements and motivations and the subsequent choices that lead to the final implementation. The event model classes and tools as in software versions Brunel v30r17, LHCb v21r12, Lbcom v5r9 and Rec v3r14 are described; these versions were used for the physics production of the 2006 data challenge (DC06)

Semiclassical Concepts in Magnetoelectronics

Semiclassical theories of electron and spin transport in metallic magnetic structures are reviewed with emphasis on the role of disorder and electronic band structures in the current perpendicular to the interface plane (CPP) transport configuration.Comment: Proceedings of the NEC Symposium on "Spin-related Quantum Transport in Mesoscopic Systems", to be published in the Journal of Materials Science and Engineering

Interplay between the magnetic anisotropy contributions of Cobalt nanowires

We report on the magnetic properties and the crystallographic structure of the cobalt nanowire arrays as a function of their nanoscale dimensions. X-ray diffraction measurements show the appearance of an in-plane HCP-Co phase for nanowires with 50 nm diameter, suggesting a partial reorientation of the magnetocrystalline anisotropy axis along the membrane plane with increasing pore diameter. No significant changes in the magnetic behavior of the nanowire system are observed with decreasing temperature, indicating that the effective magnetoelastic anisotropy does not play a dominant role in the remagnetization processes of individual nanowires. An enhancement of the total magnetic anisotropy is found at room temperature with a decreasing nanowire diameter-to-length ratio (d/L), a result that is quantitatively analyzed on the basis of a simplified shape anisotropy model.Comment: 8 pages, 4 figure