Extremal self-dual codes of length 64 through neighbors and covering radii

Naoki Chigira; Masaaki Harada; Masaaki Kitazume

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Extremal self-dual codes of length 64 through neighbors and covering radii

机译：通过邻居并覆盖半径的长度为64的极值自对偶编码

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摘要

We construct extremal singly even self-dual [64, 32, 12] codes with weight enumerators which were not known to be attainable. In particular, we find some codes whose shadows have minimum weight 12. By considering their doubly even neighbors, extremal doubly even self-dual [64, 32, 12] codes with covering radius 12 are constructed for the first time.

机译：我们使用重量枚举器构造极个别甚至偶对的[64、32、12]代码，但未知。特别是，我们发现一些阴影阴影的权重最小为12的代码。通过考虑它们的偶数偶数邻居，首次构造了覆盖半径12的极偶偶偶数[64、32、12]码。

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来源
《Designs, Codes and Crytography》 |2007年第1期|p.93-101|共9页
作者
Naoki Chigira; Masaaki Harada; Masaaki Kitazume;
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作者单位

Department of Mathematical Sciences, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
extremal self-dual code; neighbor; covering radius;

机译：极值自对码;邻居;覆盖半径;

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1. On covering radii and coset weight distributions of extremal binary self-dual codes of length 56 [J] . Ozeki M. IEEE Transactions on Information Theory . 2000,第7期

机译：关于长度为56的极值二进制自对偶码的覆盖半径和陪集权重分布
2. On covering radii and coset weight distributions of extremal binary self-dual codes of length 40 [J] . Ozeki M. Theoretical computer science . 2000,第2期

机译：关于长度为40的极值二进制自对偶码的覆盖半径和陪集权重分布
3. Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68 [J] . Gildea Joe, Hamilton Holly, Kaya Abidin, Information Processing Letters . 2020,第May期

机译：改性二次残留结构和长度为64,66和68的新极值自二元码
4. Computer Based Reconstruction of Binary Extremal Self-dual Codes of Length 32 [C] . Jon-Lark Kim Mathematical software - ICMS 2014 . 2014

机译：基于计算机的长度为32的二进制极值自对偶码的重构
5. Existence of certain extremal self-dual codes. [D] . Tsai, Han-Ping. 1992

机译：存在某些极端的自我对偶代码。
6. Erratum: Distribution of distances between DNA barcode labels in nanochannels close to the persistence length J. Chem. Phys. 142 064902 (2015) [O] . Wesley F. Reinhart, Jeff G. Reifenberger, Damini Gupta, -1

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7. On covering radii and coset weight distributions of extremal binary self-dual codes of length 40 [O] . Ozeki Michio 2000

机译：关于长度为40的极值二进制自对偶码的覆盖半径和陪集权重分布

Extremal self-dual codes of length 64 through neighbors and covering radii

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