Classifying optimal binary subspace codes of length 8,constant dimension 4 and minimum distance 6

Heinlein Daniel; Honold Thomas; Kiermaier Michael; Kurz Sascha; Wassermann Alfred

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Classifying optimal binary subspace codes of length 8,constant dimension 4 and minimum distance 6

机译：分类长度为8，恒定维数为4和最小距离为6的最佳二进制子空间代码

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摘要

We determine the maximum size A2(8,6;4) of a binary subspace code of packet length v=8, minimum subspace distance d=6, and constant dimension k=4 to be 257. There are two isomorphism types of optimal codes. Both of them are extended LMRD codes. In finite geometry terms, the maximum number of solids in PG(7,2) mutually intersecting in at most a point is 257. The result was obtained by combining the classification of substructures with integer linear programming techniques. This result implies that the maximum size A2(8,6) of a binary mixed-dimension subspace code of packet length 8 and minimum subspace distance6 is 257 as well.

机译：我们确定数据包长度为v = 8，最小子空间距离d = 6和恒定尺寸k = 4的二进制子空间代码的最大大小A2（8,6; 4）为257。最优代码有两种同构类型。它们都是扩展的LMRD代码。用有限的几何术语来说，PG（7,2）中最多相交的一个实体的最大数目是257。通过将子结构的分类与整数线性规划技术结合在一起可以得到结果。该结果意味着分组长度为8且最小子空间距离为6的二进制混合维子空间码的最大大小A2（8,6）也为257。

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来源
《Designs, Codes and Crytography》 |2019年第3期|375-391|共17页
作者
Heinlein Daniel; Honold Thomas; Kiermaier Michael; Kurz Sascha; Wassermann Alfred;
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作者单位

Univ Bayreuth, Dept Math, Bayreuth, Germany;

Zhejiang Univ, ZJU UIUC Inst, Haining, Peoples R China;

Univ Bayreuth, Dept Math, Bayreuth, Germany;

Univ Bayreuth, Dept Math, Bayreuth, Germany;

Univ Bayreuth, Dept Math, Bayreuth, Germany;

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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
关键词
Network coding; Constant-dimension codes; Subspace distance; Classification; Integer linear programming;

机译：网络编码;恒定维度代码;子空间距离;分类;整数线性规划;

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1. Classifying optimal binary subspace codes of length 8,constant dimension 4 and minimum distance 6 [J] . Heinlein Daniel, Honold Thomas, Kiermaier Michael, Designs, Codes and Crytography . 2019,第2a3期

机译：分类长度8，恒定尺寸4和最小距离6的最佳二进制子空间码
2. The smallest length of eight-dimensional binary linear codes with prescribed minimum distance [J] . Bouyukhev I., Jaffe D.B. IEEE Transactions on Information Theory . 2000,第4期

机译：具有规定最小距离的八维二进制线性代码的最小长度
3. New Constant-Dimension Subspace Codes from Maximum Rank Distance Codes [J] . Liqing Xu, Hao Chen Information Theory, IEEE Transactions on . 2018,第9期

机译：最大等级距离代码中新的恒定维子空间代码
4. Distance spectrum formula for the largest minimum hamming distance of finite-length binary block codes [C] . Ling-Hua Chang, Carol Wang, Po-Ning Chen, IEEE Information Theory Workshop . 2017

机译：有限长度二进制分组码的最大最小汉明距离的距离谱公式
5. High code rate, low-density parity-check codes with guaranteed minimum distance and stopping weight. [D] . Miller, John Andrew. 2003

机译：高码率，低密度奇偶校验码，保证最小距离和停止重量。
6. Optimally splitting cases for training and testing high dimensional classifiers [O] . Kevin K Dobbin, Richard M Simon 2011

机译：优化分割案例以训练和测试高维分类器
7. Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6 [O] . Heinlein Daniel, Honold Thomas, Kiermaier Michael, 2017

机译：分类长度为8，恒定维数为4和最小距离为6的最佳二进制子空间代码

Classifying optimal binary subspace codes of length 8,constant dimension 4 and minimum distance 6

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