Content (Tentative)

• A quick introduction to coding theory, Reed-Solomon codes, Reed-Muller codes, unique decoding and list decoding algorithms
• Locally decodable/correctable codes - Hadamard codes, Reed-Muller codes, Matching vector codes, Multivariate codes, Kopparty-Meir-Ron Zewi-Saraf's construction
• Lower bounds for locally decodable/correctable codes - 2 query LDCs, Katz-Trevisan's lower bound, lower bounds for 3 query LCCs
• Private information retrieval schemes
• Local testing of codes - Polischuk-Spielman's low degree test, line point test in the low and high error regime, the plane-point test
• Applications - explicit construction of combinatorial designs, explicit construction of condensers (Guruswami-Umans-Vadhan), derandomization from hardness (Sudan-Trevisan-Vadhan's proof), explicit construction of subspace designs (Guruswami-Kopparty)
• Other topics - distance of Dual BCH codes, decoding Reed-Muller codes on arbitrary grids.