A Topological View of Reed–Solomon Codes

hyperdiamonds: a topological view

hyperdiamonds are covalently bonded fullerenes in crystalline forms, more or less related todiamond, and having a significant amount of sp3 carbon atoms. design of severalhypothetical crystal networks was performed by using our original software programscvnet and nano-studio. the topology of the networks is described in terms of the netparameters and several counting polynomials, calculated by ...

Topological subsystem codes

A topological view of the replicon.

The replication of circular DNA faces topological obstacles that need to be overcome to allow the complete duplication and separation of newly replicated molecules. Small bacterial plasmids provide a perfect model system to study the interplay between DNA helicases, polymerases, topoisomerases and the overall architecture of partially replicated molecules. Recent studies have shown that partial...

A Simple Decoder for Topological Codes

Here we study an efficient algorithm for decoding topological codes. It is a simple form of HDRG decoder, which could be straightforwardly generalized to complex decoding problems. Specific results are obtained for the planar code with both i.i.d. and spatially correlated errors. The method is shown to compare well with existing ones, despite its simplicity.

A topological view on algebraic computation models

We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Our results can be seen as bounds on how different BSS-computability and computability in the sense of computable analysis can be. The framework for this is Weihrauch reducibility. As a consequence of our characterizations, we establish that the solvability complexity index is (mostly) inde...