Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers the original projection and lifting algorithm of Collins along with subsequent improvements. Here we report on new functionality: specifically the ability to ...

This chapter gives an introduction to algebraic coding theory and a survey of constructions of some of the well known classes of algebraic block codes such as cyclic codes, BCH codes, Reed-Solomon codes, Hamming codes, quadratic residue codes, and quasi-cyclic (QC) codes. It then describes some recent generalizations of QC codes and open problems related to them. Also discussed in this chapter ...

Polar codes were introduced by Arikan [1] in 2008 and are the first family of error-correcting codes achieving the symmetric capacity of an arbitrary binary-input discrete memoryless channel under low complexity encoding and using an efficient successive cancellation decoding strategy. Recently, non-binary polar codes have been studied, in which one can use different algebraic geometry codes to...

We present the design of S-Net, a coordination language and component technology based on stream processing. S-Net boxes integrate existing sequential code as stream-processing components into highly asynchronous concurrent streaming networks. Their construction is based on algebraic formulae built out of four network combinators. S-Net achieves a near-complete separation of concerns between ap...

Abstract State Machines (ASMs) have been widely used to specify software and hardware systems. Only a few of these specifications are executable, although there are several interpreters and some compilers. This paper introduces a compilation scheme to transform an ASM specification in the syntax of the ASM-Workbench into C++. In particular, we transform algebraic types, pattern matching, functi...

We present the design of S-Net, a coordination language and component technology based on stream processing. S-Net achieves a near-complete separation between application code, written in a conventional programming language, and coordination code written in S-Net itself. S-Net boxes integrate existing sequential code as stream-processing components into streaming networks, whose construction is...

In this paper, we study Z2Z2[u]-(1 + u)-additive constacyclic code of arbitrary length. Firstly, we study the algebraic structure of this family of codes and a set of generator polynomials for this family as a (Z2+uZ2)[x]-submodule of the ring Rα,β. Secondly, we give the minimal generating sets of this family codes, and we determine the relationship of generators between the Z2Z2[u]-(1 + u)-add...

Abstract Using algebraic techniques, one of the co-authors has designed a [155,64,20] low density parity check code based on permutation matrices. This code is quasi-cyclic by construction and hence admits a convolutional representation. A set of low density parity check convolutional codes is derived from this quasi-cyclic code and its generalizations. We investigate the performance of these c...

Mathematics has always played an important role in the design and optimization of communication systems, particularly following Shannon’s groundbreaking work in 1948 that gave theorems establishing fundamental limits on the rates of reliable communication over point-to-point channels (i.e., those involving a single transmitter-receiver pair). In order to develop fundamental bounds, concepts fro...

In this paper, we present the accelerator model of MetaFork together with the software framework that allows automatic generation of CUDA code from annotated MetaFork programs. One of the key features of this CUDA code generator is that it supports the generation of CUDA kernel code where program parameters (like number of threads per block) and machine parameters (like shared memory size) are ...