In this paper, it is proved that any algehraicgeometr ic code can be expressed as a cross section of an extended multidimensional cyclic code. Both algebraic-geometric codes and multidimensional cyclic codes are descr ibed by a unified theory of l inear block codes def ined over point sets: algebraic-geometric codes are def ined over the points of an algebraic curve, and an m-dimensional cyclic...

Many geometrical problems exist which have been researched thoroughly, but always using classical methods such as linear algebra as a framework for the problem. As linear algebra is an algebra based on coordinates and numbers as basic elements of computation, this leads to longwinded and non-universal code. Geometric algebra is an alternative formalism in which geometric objects are the basic e...

Panel zone is one of the most important elements for transferring the lateral load to other elements in Steel Moment Resistant Frames. To some extent, this element through its suitable ductile behavior with beams, that themselves have been known as ductile elements, can increase the overall ductility of SMRF. The suitable design procedure for this element and details, can highly affect the perf...

Conformal geometric algebra is a powerful tool to find geometrically intuitive solutions. We present an approach for the combination of compact and elegant algorithms with the generation of very efficient code based on two different optimization approaches with different advantages, one is based on Maple, the other one is based on the code generator Gaigen 2. With these results, we are convince...

Geometric puncturing is a method to construct new codes from a given [n, k, d]q code by deleting the coordinates corresponding to some geometric object in PG(k − 1, q). We construct [gq(4, d), 4, d]q and [gq(4, d)+1, 4, d]q codes for some d by geometric puncturing, where gq(k, d) = ∑k−1 i=0 ⌈

We study geometric variations of the discriminating code problem. In discrete version problem, a finite set points P and objects S are given in $$\mathbb {R}^d$$ . The objective is to choose subset $$S^* \subseteq S$$ minimum cardinality such that for each point $$p_i \in P$$ , $$S_i^* S^*$$ covering $$p_i$$ satisfies $$S_i^*\ne \emptyset $$ pair $$p_i,p_j $$i \ne j$$ we have S_j^*$$ continuous...