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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Good locally testable codes - Alex Lubotzky (Hebre
w University of Jerusalem)
DTSTART;TZID=Europe/London:20220725T100000
DTEND;TZID=Europe/London:20220725T105000
UID:TALK175064AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175064
DESCRIPTION:An error-correcting code is locally testable (LTC)
if there is a random tester that reads only a sma
ll number of bits of a given word and decides whet
her the word is in the code\, or at least close to
it.\nA long-standing problem asks if there exists
such a code that also satisfies the golden standa
rds of coding theory: constant rate and constant d
istance. \;Unlike the classical situation in c
oding theory\, random codes are not LTC\, so this
problem is a challenge of a new kind. \;\nWe c
onstruct such codes based on what we call (Ramanuj
an) Left/Right Cayley square complexes. \; The
se objects seem to be of independent \;group-t
heoretic interest. The \;codes built on them a
re 2-dimensional versions of the expander codes co
nstructed by Sipser and Spielman (1996). \;\nT
he main result and lecture will be self-contained.
But we hope also to explain how the seminal work
of Howard Garland ( 1972) on the cohomology of quo
tients of the Bruhat-Tits buildings of p-adic Lie
group has led to this construction ( even though i
t is not used at the end). \;\nBased on joint
work with I. Dinur\, S. Evra\, R. Livne\, and S. M
ozes.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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