Coset bounds for algebraic geometric codes

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dc.creatorDuursma, Iwan M.
dc.creatorPark, Seungkook
dc.date2008-10-15
dc.date.accessioned2026-07-07T10:10:34Z
dc.date.available2026-07-07T10:10:34Z
dc.descriptionFor a given curve X and divisor class C, we give lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors. For suitable choices of the semigroups we obtain (1) lower bounds for the size of a party A that can recover the secret in an algebraic geometric linear secret sharing scheme with adversary threshold C, and (2) lower bounds for the support A of a codeword in a geometric Goppa code with designed minimum support C. Our bounds include and improve both the order bound and the floor bound. The bounds are illustrated for two-point codes on general Hermitian and Suzuki curves.
dc.description36 pages
dc.identifierhttps://arxiv.org/abs/0810.2789
dc.identifierhttp://arxiv.org/abs/0810.2789
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171634
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject14G50, 11T71, 94B
dc.titleCoset bounds for algebraic geometric codes
dc.typetext

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