Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicstopologynatural sciencescomputer and information sciences Program(-y) 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) Temat(-y) ERC-SG-PE6 - ERC Starting Grant - Computer science and informatics Zaproszenie do składania wniosków ERC-2013-StG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-SG - ERC Starting Grant Instytucja przyjmująca BAR ILAN UNIVERSITY Wkład UE € 1 302 000,00 Adres BAR ILAN UNIVERSITY CAMPUS 52900 Ramat Gan Izrael Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kierownik naukowy Tali Kaufman Halman (Dr.) Kontakt administracyjny Estelle Waise (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko BAR ILAN UNIVERSITY Izrael Wkład UE € 1 302 000,00 Adres BAR ILAN UNIVERSITY CAMPUS 52900 Ramat Gan Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kierownik naukowy Tali Kaufman Halman (Dr.) Kontakt administracyjny Estelle Waise (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych