基于奇异线性空间的子空间码的构造

发布时间：2018-05-26 20:11

本文选题：有限域 + 奇异线性空间　；参考：《中国民航大学》2015年硕士论文

【摘要】：子空间码是非相干网络环境下网络纠错编码的一个重要研究内容,与传统的编码方法不同,子空间码将信源消息表示成一个线性空间的子空间,并把这个子空间的一组基注入到通信网络中进行信息编码、纠错、通信。由于子空间码在网络通信中具有的巨大潜力,子空间码受到了人们广泛的关注,并飞速发展。有限域上典型群的几何空间具有良好的组合结构,且容易计数,因此可以利用这些几何空间构造子空间码,研究子空间码的基本问题,完备子空间码等问题。本文基于奇异线性空间的子空间构造了子空间码,计算了所构造的子空间码的球填充界,Singleton界,Wang-Xing-Safavi-Naini界,Johnson界和Gilbert-Varshamov界,并在此基础之上得到了一类达到Wang-Xing-Safavi-Naini界的最优的子空间码。首先,文章利用奇异线性空间中的(m,0)型子空间构造了子空间码,计算了所构造的子空间码的球填充界,Singleton界,Wang-Xing-Safavi-Naini界,Johnson界和Gilbert-Varshamov界,并且得到了一类达到Wang-Xing-Safavi-Naini界的最优的子空间码((1,0),(,0),)qSm-δ+m n+l。其次,文章还利用奇异线性空间中的(m,1)型子空间构造了子空间码,计算了所构造的子空间码的球填充界,Singleton界,Wang-Xing-Safavi-Naini界,Johnson界和Gilbert-Varshamov界,并且得到了一类达到Wang-Xing-Safavi-Naini界的最优的子空间码((1,0),(,1),)qSm-δ+m n+l。
[Abstract]:Subspace code is an important part of network error correction coding in non-coherent network environment. Different from the traditional coding method, subspace code represents the source message as a linear subspace. And the subspace of a set of bases into the communication network for information coding, error correction, communication. Because of the great potential of subspace codes in network communication, subspace codes have been widely concerned and developed rapidly. The geometric space of a typical group on a finite field has a good combination structure and is easy to count. So we can use these geometric spaces to construct subspace codes and to study the basic problems of subspace codes and complete subspace codes. In this paper, we construct subspace codes based on the subspaces of singular linear spaces, and calculate the sphere filling bounds of the constructed subspace codes. The Singleton bound, Wang-Xing-Safavi-Naini bound, the Johnson bound and the Gilbert-Varshamov bound, are calculated. On this basis, we obtain a class of optimal subspace codes that reach the Wang-Xing-Safavi-Naini bound. First of all, we construct subspace codes by using the subspaces of type 0) in singular linear spaces, and calculate the sphere filling bounds of the constructed subspace codes. The Gilbert-Varshamov and Johnson bounds of the constructed subspace codes are calculated, and a class of optimal subspace codes that reach the Wang-Xing-Safavi-Naini bound is obtained. Secondly, the subspace codes are constructed by using the subspaces of type 1) in singular linear spaces. The sphere filling bounds of the constructed subspace codes are calculated. The Singleton bound and the Wang-Xing-Safavi-Naini bound and the Gilbert-Varshamov bound of the constructed subspace codes are calculated. A class of optimal subspace codes with Wang-Xing-Safavi-Naini bound is obtained. The QSm- 未 m n l. is obtained.
【学位授予单位】：中国民航大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.4

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