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UID:www.tcs.tifr.res.in/event/1049
DTSTAMP:20230914T125948Z
SUMMARY:Weight distribution and List-Decoding size of Reed-Muller codes
DESCRIPTION:Speaker: Tulasi mohan Molli\n\nAbstract: \nDetails: We will fin
 ish the remainder of previous student talk. We will begin where we ended l
 ast time.\nAbstract of the previous talk: The problem of list-decoding an 
 error-correcting code is the following:\ngiven a received word and a dista
 nce parameter find all codewords of the code that are within the given di
 stance from the received word. It is a generalization of the more common 
 notion of unique decoding.\nThe weight distribution of an error-correcting
  code counts\, for every given weight parameter\, the number of codewords
  whose hamming weight is less than the given weight parameter.\nThe codew
 ords of Reed-Muller code can be thought of as truth-tables of low degree 
 polynomials. Kaufman\, Lovett\, and Porat in their work from 2010 made a 
 novel connection between computer science techniques used for studying lo
 w-degree polynomials and these seemingly related coding theory questions 
 in the case of Reed-Muller codes.\nIn this talk\, we will see\n1) The abov
 e-mentioned result of Kaufman\, Lovett\, and Porat[KLP10] and subsequent 
 improvement of it due to Abbe\, Sphilka\, and Wigderson[ASW15] which give
  upper bounds on the weight distribution of Reed-Muller codes.\n2) A lower
  bound on the weight-distribution of Reed-Muller codes by exhibiting a co
 llection of low-degree polynomials that satisfy the weight requirement fo
 r any given weight parameter. This is joint work with Bhandari\, Harsha\,
  and Saptarishi and independently discovered by Sberlo and Shpilka[SS20].
 \n
URL:https://www.tcs.tifr.res.in/web/events/1049
DTSTART;TZID=Asia/Kolkata:20200131T140000
DTEND;TZID=Asia/Kolkata:20200131T153000
LOCATION:A-201 (STCS Seminar Room)
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