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UID:8267@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20141021T110500
DTEND;TZID=Europe/Paris:20141021T120000
DTSTAMP:20241120T210318Z
URL:https://www.i2m.univ-amu.fr/evenements/covering-sets/
SUMMARY:Arne Winterhof (RICAM\, Linz\, Austria ): Covering sets
DESCRIPTION:Arne Winterhof: For a set\n$\\cM=\\{-\\mu\,-\\mu+1\,\\ldots\, \
 \lambda\\}\\setminus\\{0\\}$ with non-negative integers λ\,μ&lt\;q not b
 oth 0\, a subset $\\cS$ of the residue class ring $\\Z_q$ modulo an intege
 r q≥1 is called a (λ\,μ\;q)-\\emph{covering set} if\n\n\\cM \\cS=\\{m
 s \\bmod q : m\\in \\cM\,\\ s\\in \\cS\\}=\\Z_q.\nSmall covering se
 ts play an important role in codes correcting limited-magnitude errors. We
  give an explicit construction of a (λ\,μ\;q)-covering set $\\cS$ which 
 is of the size q1+o(1)max{λ\,μ}−1/2 for almost all integers q≥1 and 
 of optimal size pmax{λ\,μ}−1 if q=p is prime. Furthermore\, using a bo
 und on the fourth moment of character sums of Cochrane and Shi we prove th
 e bound\n\nωλ\,μ(q)≤q1+o(1)max{λ\,μ}−1/2\,\nfor any integer q≥1
 \, however the proof of this bound is not constructive.\nhttps://arxiv.org
 /abs/1310.0120\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Arne_Winterhof.jpg
CATEGORIES:Séminaire,Ernest
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