Week 1
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Error correcting codes: Definition and bounds |
Week 2
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Reed Solomon codes: Unique decoding algorithm List decoding: General bounds for lowest possible agreement ratio between the received word and closest codewords. |
Week 3
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List decoding of Reed Solomon codes: Sudan's list-decoding Algorithm (deals with 1-sqrt(2R) agreement ratio). |
Week 4
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List decoding of Reed Solomon codes: Guruswami-Sudan list-decoding Algorithm (deals with 1-sqrt(R) agreement ratio). Linearized Polynomials: definition and properties |
Week 5
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Lower bounds for agreement in list decoding: For specific parameters, we have seen a result giving a relatively high agreement ratio for which there exist a super-polynomial number of close-enough codewords. |
Week 6
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Folded Reed Solomon codes: Definition and list decoding algorithm (almost optimal agreement ratio) |
Week 7
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Expanders, Extractors and Condensers: Definition and general properties. |
Week 8
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Expanders, Extractors and Condensers: Towards the building of an explicit extractor: An expicit bipartite "one side" expander / condensor graph |