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COCO
2010
Springer

On Matrix Rigidity and Locally Self-Correctable Codes

13 years 7 months ago
On Matrix Rigidity and Locally Self-Correctable Codes
We describe a new approach for the problem of finding rigid matrices, as posed by Valiant [Val77], by connecting it to the, seemingly unrelated, problem of proving lower bounds for linear locally self-correctable codes. This approach, if successful, could lead to a non-natural property (in the sense of Razborov and Rudich [RR97]) implying super-linear lower bounds for linear functions in the model of logarithmicdepth arithmetic circuits. Our results are based on a lemma saying that, if the generating matrix of a locally decodable code is not rigid, then it defines a locally self-correctable code with rate close to one. Thus, showing that such codes cannot exist will prove that the generating matrix of any locally decodable code (and in particular Reed Muller codes) is rigid.
Zeev Dvir
Added 15 Aug 2010
Updated 15 Aug 2010
Type Conference
Year 2010
Where COCO
Authors Zeev Dvir
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