本文選題：Ferrers圖 + 秩度量碼　； 參考：《蘇州大學(xué)》2016年碩士論文

【摘要】：子空間碼可用于隨機(jī)網(wǎng)絡(luò)編碼,其存在性是近年來編碼理論中的一個(gè)熱點(diǎn)問題.常維數(shù)碼作為一類特殊而重要的子空間碼越來越受到人們的重視.多重構(gòu)造方法作為構(gòu)造常維數(shù)碼的一種主要方法,它主要依賴于skeleton碼的選擇以及對應(yīng)的Ferrers圖秩度量碼的存在性.本文第二章主要給出了兩種構(gòu)作Ferrers圖秩度量碼的方法,利用點(diǎn)膨脹和最大距離可分碼填充的方法以及通過對小的Ferrers圖進(jìn)行適當(dāng)組合的方法,得到大的Ferrers圖秩度量碼.并且利用這兩種構(gòu)作方法改進(jìn)了幾類Ferrers圖秩度量碼的下界,其中一類Ferrers圖秩度量碼的維數(shù)達(dá)到了最優(yōu).第三章主要通過改進(jìn)多重構(gòu)造方法中skeleton碼的選擇,給出了改進(jìn)后的多重構(gòu)造方法,并且利用此方法改進(jìn)了幾個(gè)常維數(shù)碼的下界.
[Abstract]:Subspace codes can be used in random network coding. The existence of subspace codes is a hot issue in coding theory in recent years. As a special and important subspace code, the constant dimension code has been paid more and more attention. As a main method of constructing constant dimensional codes, multiplex construction mainly depends on the selection of skeleton codes and the existence of corresponding rank metric codes of Ferrers graphs. In the second chapter, we give two methods to construct rank metric codes of Ferrers graphs. By using the methods of point expansion, maximum distance divisible code filling and proper combination of small Ferrers graphs, we obtain large rank metric codes of Ferrers graphs. The lower bounds of several kinds of rank metric codes of Ferrers graphs are improved by using these two methods, in which the dimension of rank metric codes of a class of Ferrers graphs is optimal. In chapter 3, the improved multiplex construction method is presented by the selection of skeleton codes in the improved multiplex construction method, and the lower bounds of several constant dimensional codes are improved by this method.
【學(xué)位授予單位】：蘇州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O157.4

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相關(guān)碩士學(xué)位論文 前1條

1 劉雙慶;Ferrers圖秩度量碼的構(gòu)造[D];蘇州大學(xué);2016年

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本文編號：1998096