[数学] 代数几何码的陪集界 [推广有奖]

摘要翻译：
对于给定的曲线X和除子类C，我们给出了除子a的次的下界，使得a和A-C属于指定的除子半群。对于半群的适当选择，我们得到了（1）在具有敌手门限C的代数几何线性秘密共享方案中，可恢复秘密的甲方规模的下界；（2）在具有设计最小支持度C的几何Goppa码中，码字支持度a的下界。我们的下界包括并改进了序界和底界。给出了一般Hermitian曲线和Suzuki曲线上两点码的界。
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英文标题：
《Coset bounds for algebraic geometric codes》
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作者：
Iwan M. Duursma (University of Illinois at Urbana-Champaign),
  Seungkook Park (University of Cincinnati)
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
  For 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.
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PDF链接：
https://arxiv.org/pdf/0810.2789