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Lecture 12 (the last one)

January 31, 2013

Today was the last lecture of the course! How would your weekends look like without our Thursday’s circuit lower bounds lectures?  Who knows.. Well, don’t forget we have the end of the semester talks ahead of us, and I suggest you’ll visit at least two or three talks out of the ~20. This is a good and somewhat informal chance to hear of classic and important results.

In today’s lecture we continued to talk about Matrix Rigidity. We showed how to construct modest, though state-of-the-art rigid matrices from Algebraic-Geometric codes, using the untouched sub-matrix method. We then defined locally decodable codes (LDC) and locally correctable codes, or LCC (see a recent survey by Sergey Yekhanin), and showed a result by Zeev Dvir, that roughly states that if the generating matrix of a (known construction) of an LDC is not rigid, then there exists an LCC with large dimension (and somewhat nonstandard query and distance parameters). Therefore, an upper bound on the dimension of an LCC with such parameters implies that the generating matrix of known LDC codes are rigid enough to yield linear-circuit lower bounds.

That’s it. I want to thank you all for coming to the lectures and contributed your thoughts and questions to the discussion. I had a great time!

Gil

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