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UID:www.tcs.tifr.res.in/event/1701
DTSTAMP:20260312T060149Z
SUMMARY:GM-MDS Conjecture: MDS matrices over small fields
DESCRIPTION:Speaker: Soham Chatterjee (TIFR)\n\nAbstract: \nAn MDS matrix i
 s a matrix whose minors all have full rank. A question arising in coding t
 heory is what zero patterns can MDS matrices have. There is a natural comb
 inatorial characterization (called the MDS condition) which is necessary o
 ver any field\, as well as sufficient over very large fields by a probabil
 istic argument. Dau et al. conjectured that the MDS condition is sufficien
 t over small fields as well\, where the construction of the matrix is alge
 braic instead of probabilistic. This is known as the GM-MDS conjecture. Co
 ncretely\, if a k × n zero pattern satisfies the MDS condition\, then the
 y conjecture that there exists an MDS matrix with this zero pattern over a
 ny field of size |F| ≥ n + k - 1. In this talk\, we will discuss the GM-
 MDS conjecture and a more general version proposed by Shachar Lovett in hi
 s FOCS 2018 paper. We will also try to see this general conjecture in a sp
 ecial case\, which implies the original GM-MDS conjecture as a special cas
 e and will also try to prove the special case.\nLink of paper: https://arx
 iv.org/abs/1803.02523\n
URL:https://www.tcs.tifr.res.in/web/events/1701
DTSTART;TZID=Asia/Kolkata:20260313T160000
DTEND;TZID=Asia/Kolkata:20260313T170000
LOCATION:A-201 (STCS Seminar Room)
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