Locally testable codes with constant rate, distance, and locality
An outstanding open problem in the theory of error correcting codes has been whether there exist locally testable codes with constant rate, constant distance, and constant locality. In this talk this I will describe a recent construction of such codes based on a new two-dimensional complex which we call a left-right Cayley complex. This is based on a joint work with Irit Dinur, Ron Liven, Alex Lubotzky and Shahar Mozes.