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List-decoding Homomorphism Codes

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자료유형	E-Book
개인저자	Wuu, Angela.
단체저자명	The University of Chicago. Mathematics and Computer Science.
서명/저자사항	List-decoding Homomorphism Codes.
발행사항	[S.l.] : The University of Chicago., 2018
발행사항	Ann Arbor : ProQuest Dissertations & Theses, 2018
형태사항	160 p.
소장본 주기	School code: 0330.
ISBN	9780438088016
일반주기	Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B. Adviser: Laszlo Babai.
요약	The codewords of the homomorphism code aHom( G,H) are the affine homomorphisms between two finite groups, G and H, generalizing Hadamard codes. Following the work of Goldreich--Levin (1989), Grigorescu et al. (2006), Dinur et al. (2008), and G
요약	Our main result is efficient local list-decoding for the permutation representations of alternating groups (i.e., when the codomain is a symmetric group Sm) under the restriction that the domain G=An is paired with codomain H=Sm satisfying m <
요약	The limitations on the codomain in the latter case reflect a gap between uniquely identifying a homomorphism in aHom(An, H) and determining the homomorphism on generators of the whole group. This phenomenon is new and is sure to appear again for
요약	For this reason, we introduce an intermediate algorithmic model we call Certificate List-Decoding that avoids the HomExt bottleneck and works in the alternating versus arbitrary setting.
요약	Our new combinatorial tools allow us to play on the relatively well-understood top layers of the subgroup lattice of the domain, avoiding the dependence on the codomain, a bottleneck in previous work. We also introduce ``mean-list-decoding,'' a
요약	While motivated by bridging the mentioned gap in list-decoding, HomExt is also of independent interest, both as a problem in computational group theory and as a new and natural problem in NP of unsettled complexity status.
요약	We consider the case H=Sm (the symmetric group of degree m), i.e., gamma : G &rarr
요약	We are most concerned with the case G=A n (the alternating group of degree n) for variable n under the assumption that the index of M in G is bounded by poly(n). We solve this case in polynomial time for all m < 2n-1/"the square root of" n. This
일반주제명	Mathematics. Computer science.
언어	영어
기본자료 저록	Dissertation Abstracts International79-11B(E). Dissertation Abstract International
대출바로가기	http://www.riss.kr/pdu/ddodLink.do?id=T14997882