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UID:93ff4ccef571024bb8fe9a8fb170891a
CATEGORIES:Experimental Mathematics Seminar
CREATED:20210414T132411
SUMMARY:Locality preserving hash functions, a partial order and tiles in binary space
LOCATION:zoom
DESCRIPTION:Abstract: A "tile" in the space B^n of bit vectors of length n, is a subset
  S of B^n, such that there is another subset A of B^n so that every element
  of B^n can be written uniquely in the form a + s, where a in A and s in S.
  A particular class of tiles are the subsets of minimum weight elements in 
 the cosets of a linear code over GF(2). In systematically investigating loc
 ality preserving hash functions, we generated the list of all possible tile
 s of cardinality <=64 satisfying a certain optimality condition. All but
  6 of them turned out to be the sets of minimum weight elements described a
 bove. Attempts to prove the same for the remaining 6 remained elusive. Inst
 ead we found two computational criteria -- one using linear programming, an
 d the other using combinatorial bin packing, which showed that the remainin
 g 6 could not be tiles. \n[Joint with Don Coppersmith, Dan Gordon and Peter
  Ostapenko]\n
X-ALT-DESC;FMTTYPE=text/html:<p style="text-align: left; color: #000000; text-transform: none; text-inde
 nt: 0px; letter-spacing: normal; font-family: Times New Roman; font-size: 1
 6px; font-variant: normal; font-weight: 400; text-decoration: none; word-sp
 acing: 0px; white-space: normal; orphans: 2;"><em>Abstract</em>: A "tile" i
 n the space B^n of bit vectors of length n, is a subset S of B^n, such that
  there is another subset A of B^n so that every element of B^n can be writt
 en uniquely in the form a + s, where a in A and s in S. A particular class 
 of tiles are the subsets of minimum weight elements in the cosets of a line
 ar code over GF(2). In systematically investigating locality preserving has
 h functions, we generated the list of all possible tiles of cardinality &lt
 ;=64 satisfying a certain optimality condition. All but 6 of them turned ou
 t to be the sets of minimum weight elements described above. Attempts to pr
 ove the same for the remaining 6 remained elusive. Instead we found two com
 putational criteria -- one using linear programming, and the other using co
 mbinatorial bin packing, which showed that the remaining 6 could not be til
 es.&nbsp;</p><p style="text-align: left; color: #000000; text-transform: no
 ne; text-indent: 0px; letter-spacing: normal; font-family: Times New Roman;
  font-size: 16px; font-variant: normal; font-weight: 400; text-decoration: 
 none; word-spacing: 0px; white-space: normal; orphans: 2;">[Joint with Don 
 Coppersmith, Dan Gordon and Peter Ostapenko]</p>
CONTACT:Victor S. Miller -- IDA Center for Communications Research, Princeton
X-EXTRAINFO:https://rutgers.zoom.us/j/94346444480\npassword:  6564120420 
DTSTAMP:20260828T110907
DTSTART;TZID=America/New_York:20210429T170000
DTEND;TZID=America/New_York:20210429T180000
SEQUENCE:0
TRANSP:OPAQUE
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