The use of color in QR codes brings extra data capacity, but also inflicts tremendous challenges on the decoding process due to chromatic distortion—cross-channel color interference and illumination variation. Particularly, we further discover a new type of chromatic distortion in high-density color QR codes—cross-module color interference—caused by the high density which also makes the geometr...

Any geometric algorithm can be dissected into combinatorial parts and geometric parts. The two parts intertwine in both the description and the implementation of the algorithm. We consider the benefits of relaxing this tight coupling. Coordinate freedom is widely considered the most important principle in designing and implementing geometric systems. By ensuring that client code not manipulate ...

For an [n, k, d]q code C, we define a mapping wC from PG(k − 1, q) to the set of weights of C via a generator matrix of C. We give a geometric aspect derived from wC to investigate the extendability of linear codes. We survey known extension theorems and some recent results.

We develop Gray code enumeration schemes for geometric straight-line graphs in the plane. The considered graph classes include plane graphs, connected plane graphs, and plane spanning trees. Previous results were restricted to the case where the underlying vertex set is in convex position.

The focus of the this work is a simplified integration of algorithms expressed in Geometric Algebra (GA) in 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.

We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from noncommutative geometry, arising from rational noncommutative tori and finite abelian group actions on Cuntz algebras and fractals associated to the clas...

This library manipulates ensembles of cycles (quadrics), which are interrelated through certain geometric relations (to be orthogonal, to be tangent, etc.). The code operates with numeric and symbolic data of cycles in spaces of arbitrary dimensionality and metrics with any signatures. In the two-dimensional case illustrations and animations can be produced.

In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P ⊂ R 2 . The bounds involve a geometric invariant L(P ) , called the full Minkowski length of P which can be easily computed for any given P .