Block diagonalization for algebra's associated with block codes

For a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the (non)binary Hamming cube, and algebras arising in SDP-hierarchies for coding bounds using moment matrices. We give a computationally efficient block diagonalization of A in terms of a given block diagonalization of B, and work out some examples, including the Terwilliger algebra of the binary- and nonbinary Hamming cube. As a tool we use some basic facts about representations of the symmetric group.Comment: 16 page

Runtime-Flexible Multi-dimensional Arrays and Views for C++98 and C++0x

Multi-dimensional arrays are among the most fundamental and most useful data structures of all. In C++, excellent template libraries exist for arrays whose dimension is fixed at runtime. Arrays whose dimension can change at runtime have been implemented in C. However, a generic object-oriented C++ implementation of runtime-flexible arrays has so far been missing. In this article, we discuss our new implementation called Marray, a package of class templates that fills this gap. Marray is based on views as an underlying concept. This concept brings some of the flexibility known from script languages such as R and MATLAB to C++. Marray is free both for commercial and non-commercial use and is publicly available from www.andres.sc/marrayComment: Free source code availabl

High performance FORTRAN without templates: An alternative model for distribution and alignment

Language extensions of FORTRAN are being developed which permit the user to map data structures to the individual processors of distributed memory machines. These languages allow a programming style in which global data references are used. Current efforts are focussed on designing a common basis for such languages, the result of which is known as High Performance Fortran (HPF). One of the central debates in the HPF effort revolves around the concept of templates, introduced as an abstract index space to which data could be aligned. A model for the mapping of data which provides the functionality of High Performance Fortran distributions without the use of templates is presented