Let q be a power of an odd prime number and Fq be the finite field with q elements. We will construct a binary spherical code from an algebraic curve C defined over Fq and a rational divisor G on C, as the twist by the quadratic character 11 of the Goppa code L(G). The computation of the parameters of this code is based on the study of some character sums. 0. Introduction. In a previous paper (...

The focus of this work is a simplified integration of algorithms expressed in Geometric Algebra (GA) into modern high level computer languages, namely C++, OpenCL and CUDA. A high runtime performance in terms of GA is achieved using symbolic simplification and code generation by a precompiler that is directly integrated into CMake-based build toolchains. Finally, we demonstrate how to interface...

‎‎a natural generalization of two dimensional cyclic code ($t{tdc}$) is two dimensional skew cyclic code‎. ‎it is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $r_n:=f[x,y;rho,theta]/_l$‎. ‎in this paper we characterize the left ideals of the ring $r_n$ with two methods and find the generator matrix for two dimensional s...

Multigrid methods are among the fastest numerical algorithms for the solution of large sparse systems of linear equations. While these algorithms exhibit asymptotically optimal computational complexity, their efficient parallelisation is hampered by the poor computation-to-communication ratio on the coarse grids. Our contribution discusses parallelisation techniques for geometric multigrid meth...

Multigrid methods are among the fastest numerical algorithms for the solution of large sparse systems of linear equations. While these algorithms exhibit asymptotically optimal computational complexity, their efficient parallelisation is hampered by the poor computation-to-communication ratio on the coarse grids. Our contribution discusses parallelisation techniques for geometric multigrid meth...

Broaching is a very common manufacturing process for the machining of internal or external complex shapes into parts. Due to the process geometry, broaching tool is the most critical parameter of the broaching process. Therefore, optimal design of the tools is needed in order to improve the productivity of the process. In this paper, a methodology is presented for optimal design of the broachin...

For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We use our ideal and a geometric characterization to determine the number of small-weight codewords for some families of Hermitian codes over any Fq. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with d ≤ q. For such codes w...

This paper is aimed to investigate the design of an optimized neutron radiography system that utilizes the flux of a reactor. Moderation, collimation aspects are studied. A Monte Carlo code, MCNP4C, was utilized to achieve a maximum and more homogenous neutron flux in the collimator outlet next to the image plane, taking into account geometric characteristics. It was possible to obtain a normal...

We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of particular codes defined using a linear combination o...