Objetivo Error correcting codes play a fundamental role in computer science. Good codes are codes with rate and distance that are asymptotically optimal. Some of the most successful good codes are constructed using expander graphs. In recent years a new notion of {\em robust} error correcting codes, known as locally testable codes (LTCs), has emerged. Locally testable codes are codes in which a proximity of a vector to an error correcting code can be achieved by probing the vector in {\em constant} many locations (independent of its length). LTCs are at the heart of Probabilistically Checkable Proofs (PCPs) and their construction has been sought since the discovery of the PCP theorem in the early 1990s.Despite 20 years of research, it is still widely open whether good locally testable codes exist. LTCs present completely new challenge to the field of error correcting codes. In the old paradigm a random code is a good code and the main focus was to construct explicit codes that imitate the random code. However, a random code is not an LTC. Thus, contrary to traditional codes, there are no natural candidates for LTCs. The known constructions of robust codes are ad hoc, and there is a lack of theory that explains their existence.The goal of the current research plan is to harness the emerging field of higher dimensional expanders and their topological properties for a systematic study of robust error correcting codes. Higher dimensional expanders are natural candidates for obtaining robust codes since they offer a strong form of redundancy that is essential for robustness. Such form of redundancy is lacking by their one dimensional analogue (i.e. expander graphs). Hence, the known expander codes are not robust. We expect that our study will draw new connections between error correcting codes, high dimensional expanders, topology and probability that will shed new light on these fields, and in particular, will advance the constructing of good and robust codes. Ámbito científico natural sciencesmathematicspure mathematicstopologynatural sciencescomputer and information sciences Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-SG-PE6 - ERC Starting Grant - Computer science and informatics Convocatoria de propuestas ERC-2013-StG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida BAR ILAN UNIVERSITY Aportación de la UE € 1 302 000,00 Dirección BAR ILAN UNIVERSITY CAMPUS 52900 Ramat Gan Israel Ver en el mapa Tipo de actividad Higher or Secondary Education Establishments Investigador principal Tali Kaufman Halman (Dr.) Contacto administrativo Estelle Waise (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo BAR ILAN UNIVERSITY Israel Aportación de la UE € 1 302 000,00 Dirección BAR ILAN UNIVERSITY CAMPUS 52900 Ramat Gan Ver en el mapa Tipo de actividad Higher or Secondary Education Establishments Investigador principal Tali Kaufman Halman (Dr.) Contacto administrativo Estelle Waise (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos