On Matrix Rigidity and Locally Self-correctable Codes

We describe a new connection between the problem of finding rigid matrices, as posed by Valiant (MFCS 1977), and the problem of proving lower bounds for linear locally correctable codes. Our result shows that proving linear lower bounds on locally correctable codes with super-logarithmic query complexity will give new constructions of rigid matrices. The interest in constructing rigid matrices is their connection to circuit lower bounds.