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Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes

机译：一点aG的Lee-O'sullivan列表解码的推广代码

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摘要

We generalize the list decoding algorithm for Hermitian codes proposed by Leeand O'Sullivan based on Gr\"obner bases to general one-point AG codes, under anassumption weaker than one used by Beelen and Brander. Our generalizationenables us to apply the fast algorithm to compute a Gr\"obner basis of a moduleproposed by Lee and O'Sullivan, which was not possible in anothergeneralization by Lax.

机译：在比Beelen和Brander使用的假设弱的假设下，我们将基于Leeb O'Sullivan基于Gr'obner基提出的Hermitian码的列表解码算法推广到一般的单点AG码。我们的推广使我们能够将快速算法应用于计算Lee和O'Sullivan提出的模块的Gr'obner基础，这在Lax的另一个概括中是不可能的。

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Matsumoto, Ryutaroh; Ruano, Diego; Geil, Olav;
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年度 2013
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正文语种 {"code":"en","name":"English","id":9}
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专利

1. Generalization of the Lee-O'Sullivan list decoding for one-point AG codes [J] . Ryutaroh Matsumoto, Diego Ruano, Olav Geil urnal of Symbolic Computation . 2013,第auga期

机译：单点AG码的Lee-O'Sullivan列表解码的一般化
2. Miura's generalization of one-point AG codes is equivalent to hoholdt, van lint and pellikaan's generalization [J] . Ryutaroh Matsumoto IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences . 1999,第10期

机译：Miura对单点AG代码的推广等同于hoholdt，van lint和pellikaan的推广
3. A Generalization Belief Propagation Decoding Algorithm for Polar Codes Based on Particle Swarm Optimization [J] . YingxianZhang, AijunLiu, XiaofeiPan, Mathematical Problems in Engineering: Theory, Methods and Applications . 2014,第7期

机译：基于粒子群算法的极化码广义置信传播解码算法
4. List decoding algorithms based on Gröbner bases for general one-point AG codes [C] . Geil, Olav, Matsumoto, Ryutaroh, Ruano, Diego IEEE International Symposium on Information Theory;ISIT 2012 . 2012

机译：基于Gröbner基的通用单点AG码列表解码算法
5. VLSI architectures for turbo code decoders, LDPC code decoders and list sphere decoders [D] . Zhang, Yuping 2007

机译：用于Turbo代码解码器，LDPC代码解码器和列表球形解码器的VLSI架构
6. List Decoding of Arıkan’s PAC Codes [O] . Hanwen Yao, Arman Fazeli, Alexander Vardy 2021

机译：列出Arıkan的PAC码的解码
7. Generalization of the Lee-O'Sullivan list decoding for one-point AG codes [O] . Matsumoto, Ryutaroh, Ruano, Diego, Geil, Hans Olav 2013

机译：Lee-O'sullivan列表解码一点aG代码的推广
8. Decodage Pondere des Codes en Blocs et Quelques Sujets sur la Complexite du Decodage (Weighted Decoding of Block Codes and Some Topics on Decoding Complexity) [R] . Fang, J. 1987

机译：Decodage pondere des Codes en Blocs et Quelques sujets sur la Complexite du Decodage（块编码的加权解码和解码复杂性的一些主题）

Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes

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