AADLib, A Library of Reusable AADL Models

The SAE Architecture Analysis and Design Language is now a well-established language for the description of critical embedded systems, but also cyber-physical ones. A wide range of analysis tools is already available, either as part of the OSATE tool chain, or separate ones. A key missing elements of AADL is a set of reusable building blocks to help learning AADL concepts, but also experiment already existing tool chains on validated real-life examples. In this paper, we present AADLib, a library of reusable model elements. AADLib is build on two pillars: 1/ a set of ready-to- use examples so that practitioners can learn more about the AADL language itself, but also experiment with existing tools. Each example comes with a full description of available analysis and expected results. This helps reducing the learning curve of the language. 2/ a set of reusable model elements that cover typical building blocks of critical systems: processors, networks, devices with a high level of fidelity so that the cost to start a new project is reduced. AADLib is distributed under a Free/Open Source License to further disseminate the AADL language. As such, AADLib provides a convenient way to discover AADL concepts and tool chains, and learn about its features

On products and powers of linear codes under componentwise multiplication

In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that could otherwise probably not fit in a regular research paper. On the other hand, more advanced results and applications are only quickly mentioned with references to the literature. We also point out a few open problems. Our presentation alternates between two points of view, which the theory intertwines in an essential way: that of combinatorial coding, and that of algebraic geometry. In appendices that can be read independently, we investigate topics in multilinear algebra over finite fields, notably we establish a criterion for a symmetric multilinear map to admit a symmetric algorithm, or equivalently, for a symmetric tensor to decompose as a sum of elementary symmetric tensors.Comment: 75 pages; expanded version of a talk at AGCT-14 (Luminy), to appear in vol. 637 of Contemporary Math., AMS, Apr. 2015; v3: minor typos corrected in the final "open questions" sectio

An upper bound of Singleton type for componentwise products of linear codes

We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical Singleton bound.Comment: 9 pages; major improvements in v3: now works for an arbitrary number of codes, and the low-weight codeword can be taken in product form; submitted to IEEE Trans. Inform. Theor

Asymptotically good binary linear codes with asymptotically good self-intersection spans

If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for C ranging in this family, the C^2 also form an asymptotically good family. For this we use algebraic-geometry codes, concatenation, and a fair amount of bilinear algebra. More precisely, the two main ingredients used in our construction are, first, a description of the symmetric square of an odd degree extension field in terms only of field operations of small degree, and second, a recent result of Garcia-Stichtenoth-Bassa-Beelen on the number of points of curves on such an odd degree extension field.Comment: 18 pages; v2->v3: expanded introduction and bibliography + various minor change