Title: Combinatorial Construction of Locally Testable Codes
Speaker: Or Meir, IAS
Date: Tuesday, February 5, 2013 2:00pm
Location: Hill Center, Room 124, Rutgers University, Busch Campus, Piscataway, NJ
An error correcting code is said to be locally testable if there is a test that can check whether a given string is a codeword of the code, or rather far from the code, by reading only a constant number of symbols of the string. Locally Testable Codes (LTCs) were first explicitly studied by Goldreich and Sudan (J. ACM 53(4)) and since then several constructions of LTCs were suggested. While the best known construction of LTCs achieves very efficient parameters, it relies heavily on algebraic tools and on PCP machinery. We present a new and arguably simpler construction of LTCs that uses only elementary linear algebra. Finally, our construction matches the parameters of the best known construction.