本文選題：有限域 + 奇異線性空間�。� 參考：《中國民航大學(xué)》2015年碩士論文

【摘要】：子空間碼是非相干網(wǎng)絡(luò)環(huán)境下網(wǎng)絡(luò)糾錯編碼的一個重要研究內(nèi)容,與傳統(tǒng)的編碼方法不同,子空間碼將信源消息表示成一個線性空間的子空間,并把這個子空間的一組基注入到通信網(wǎng)絡(luò)中進(jìn)行信息編碼、糾錯、通信。由于子空間碼在網(wǎng)絡(luò)通信中具有的巨大潛力,子空間碼受到了人們廣泛的關(guān)注,并飛速發(fā)展。有限域上典型群的幾何空間具有良好的組合結(jié)構(gòu),且容易計數(shù),因此可以利用這些幾何空間構(gòu)造子空間碼,研究子空間碼的基本問題,完備子空間碼等問題。本文基于奇異線性空間的子空間構(gòu)造了子空間碼,計算了所構(gòu)造的子空間碼的球填充界,Singleton界,Wang-Xing-Safavi-Naini界,Johnson界和Gilbert-Varshamov界,并在此基礎(chǔ)之上得到了一類達(dá)到Wang-Xing-Safavi-Naini界的最優(yōu)的子空間碼。首先,文章利用奇異線性空間中的(m,0)型子空間構(gòu)造了子空間碼,計算了所構(gòu)造的子空間碼的球填充界,Singleton界,Wang-Xing-Safavi-Naini界,Johnson界和Gilbert-Varshamov界,并且得到了一類達(dá)到Wang-Xing-Safavi-Naini界的最優(yōu)的子空間碼((1,0),(,0),)qSm-δ+m n+l。其次,文章還利用奇異線性空間中的(m,1)型子空間構(gòu)造了子空間碼,計算了所構(gòu)造的子空間碼的球填充界,Singleton界,Wang-Xing-Safavi-Naini界,Johnson界和Gilbert-Varshamov界,并且得到了一類達(dá)到Wang-Xing-Safavi-Naini界的最優(yōu)的子空間碼((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.
【學(xué)位授予單位】：中國民航大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O157.4

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 曹張華;唐元生;;安全網(wǎng)絡(luò)編碼綜述[J];計算機(jī)應(yīng)用;2010年02期

，

本文編號：1938742