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March 14, Wednesday
12:00 – 13:00

While many of the classical codes are cyclic, a long standing conjecture asserts that there are no 'good' cyclic codes. In recent years the intrest in symmetric codes has been promoted by Kaufamn, Sudan, Wigderson and others (where symmetric means that the acting group can be any group). Answering their main question (and in contrary to the common expectation), we show that there DO exist symmetric good codes. In fact, our codes satisfy all the "golden standards" of coding theory. Our construction is based on the Ramanujan graphs contructed by Lubotzky-Samuels-Vishne as a special case of Ramanujan complexes. The crutial point is that these graphs are edge transitive and not just vertex transitive as in prevous constructions of Ramanujan graphs. All notions will be explained. Joint work with Tali Kaufman.