Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [8]. He had the beautiful idea of associating to a curve X defined over Fq, the finite field with q elements, a code C. This code, called Algebraic-Geometric (AG) code, is constructed from two divisors D and G on X , where one of them, say D, is the sum of n distinct Fq-rational points of X . It turns out th...

Decoding geometric Goppa codes can be reduced to solving the key congruence of a received word in an affine ring. If the code length is smaller than the number of rational points on the curve, then this method can correct up to 12(d ∗ − 1)− s errors, where d∗ is the designed minimum distance of the code and s is the Clifford defect. The affine ring with respect to a place P is the set of all ra...

Multiscale optimization is an attractive research field recently. For the most of optimization tools, design parameters should be updated during a close loop. Therefore, a simple Python code is programmed to obtain effective properties of Representative Volume Element (RVE) under Periodic Boundary Conditions (PBCs). It can compute the mechanical properties of a composite with a periodic structu...

Linear and nonlinear gyrokinetic simulations with the GENE code F. Jenko et al., Phys. Plasmas 7, 1904 2000 for tokamak edge plasmas as well as for stellarator core plasmas are presented, shedding light on the behavior of plasma microturbulence under near-separatrix or nonaxisymmetric conditions. To this aim, the required geometric coefficients are inferred directly from the magnetohydrodynamic...

Quantum information processors need to be protected against errors and faults. One of the most widely considered fault-tolerant architecture is based on surface codes. While the general principles of these codes are well understood and basic code properties such as minimum distance and rate are easy to characterize, a code’s average performance depends on the detailed geometric layout of the qu...

In recent years, Geometric Algebra (GA) has become more and more popular in fields of science and engineering due to its potential for compact algorithms. However, the execution of GA algorithms and the related need for high computational power is still the limiting factor for these algorithms to be used in practice. Therefore, it would be desirable to automatically detect parts that can be cal...

The study of spatial cognition has benefited greatly from a technique known as the disorientation procedure. This procedure was originally used with rats to show that they relied on the geometry of an enclosed space to locate a target hidden in that space. Disorientation has since been used with a variety of mobile animals, including human children, to examine the coding of geometric informatio...

We present a novel error correcting code and decoding algorithm which have construction similar to expander codes. The code is based on a bipartite graph derived from the subsumption relations of finite projective geometry, and ReedSolomon codes as component codes. We use a modified version of well-known Zemor’s decoding algorithm for expander codes, for decoding our codes. By derivation of geo...