本文選題：二維光正交碼 + 變重量��； 參考：《廣西師范大學(xué)》2017年碩士論文

【摘要】：1989 年 Salehi 提出了一維常重量光正交碼(One-Dimensional Constant-Weight Op-tical Orthogonal Code,1D CWOOC)的概念,它作為一種簽名序列被應(yīng)用于光碼分多址(OCDMA)系統(tǒng).由于一維常重量光正交碼不能滿足多種服務(wù)質(zhì)量(QoS)需求,Yang于1996 年引入了一維變重量光正交碼(One-Dimensional Variable-Weight Optical Orthogonal Code,1D VWOOC)用于OCDMA系統(tǒng).隨著社會的高速發(fā)展,人們對不同類型信息的需求逐漸提高,這就要求產(chǎn)生高速率、大容量、不同誤碼率的OCDMA系統(tǒng).為了給光正交碼擴(kuò)容,Yang于1997年提出了二維常重量光正交碼(Two-Dimensional Constant-Weight Optical Orthogonal Code,2D CWOOC),但類似于一維常重量光正交碼,二維常重量光正交碼也只能滿足單一質(zhì)量的服務(wù)需求.為了解決這一問題,Yang于2001年引入二維變重量光正交碼(Two-Dimensional Variable-Weight Optical Orthogonal Code,2D VWOOC).下面給出二維變重量光正交碼的定義.設(shè)W ={w1,w2,...,wr}為正整數(shù)集合,Λa =(λa(1),λa(2),...,λa(r))為正整數(shù)數(shù)組,Q =(q1,q2,...,qr)為正有理數(shù)數(shù)組且(?).不失一般性,我們假設(shè)w1w2...wr.二維(u×v,W,Λa,λc,Q)變重量光正交碼或(u×v,W,Λa,λc,Q)-OOC C,是一簇u×v的(0,1)矩陣(碼字),并且滿足以下三個性質(zhì):(1)碼字重量分布:C中的碼字所具有的漢明重量均在集合W中,且C恰有qi|C|個重量為wi的碼字,1≤i≤r,即qi為重量等于wi的碼字占總碼字個數(shù)的百分比,因而(?).(2)周期自相關(guān)性:對任意矩陣X∈C.其漢明重量wk∈W,整數(shù)τ，0τv-1,(3)周期互相關(guān)性:對任意兩個不同矩陣X,Y∈C,整數(shù)τ,0≤τ＜v-1,上述符號(?)表示對v取模運(yùn)算.若λa(1)=λa(2)=...=λa(r)=λa,我們將(u×v,W,Λa,λc,Q)-OOC 記為(u×v,W,Λa,λc,Q)-OOC.若λa=λc=λ.則記為(u×v,W,Λa,λc,Q)-OOC.若 Q =(a1/b·a2/b,...,ar/b)且gcd(a1,a2,...,ar)= 1:則稱Q是標(biāo)準(zhǔn)的,顯然,(?).若W = {w},則Q =(1).所以，，常重量的(u×v,w,λ)-OOC可以看作是(u×v,{w},λ,(1))-OOC.對于光正交碼,當(dāng)它的碼字個數(shù)達(dá)到最大值時稱其為最優(yōu)的.而對于最優(yōu)(u×v,W,1,Q)-OOC的構(gòu)造己有一些成果,但就作者目前所知對于最優(yōu)二維變重量光正交碼的存在性結(jié)果不多,本文將做繼續(xù)研究并且得到以下主要結(jié)果.定理1.1 如果在Zv上存在斜Starter,則存在1-正則且最優(yōu)(6×v,{3,4},1,(4/5,1/5))-OOC.定理1.2 如果在Zv上存在斜Starter,則存在1-正則(6×v,{3,4},1,(2/3,1/3))-OOC.定理1.3 如果在Zv上存在斜Starter,則存在1-正則(9×v,{3,4},1,(7/8,1/8))-OOC.定理1.4 設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 4),則存在1-正則且最優(yōu)(3×v,{3,4},1,(4/5,1/5))-OOC.定理1.5 設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 4),則存在1-正則且最優(yōu)(6×v,{3,4},1,(6/7,1/7))-OOC.定理1.6 設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 4).則存在1-正則且最優(yōu)(6×v,{3,4},1,(10/11,1/11))-OOC.定理1.7 設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 4).則存在1-正則且最優(yōu)(6×v,{3,4},1,(22/23,1/23))-OOC.定理1.8 設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 6),則存在1-正則且最優(yōu)(6×v,{3,4},1,(1/2,1/2))-OOC.定理1.9設(shè)v為正整數(shù)且u的每個質(zhì)因子p≡1(mod 6),則存在1-正則且最優(yōu)(4 × v,{3,4},1,(2/5,3/5))-OOC.定理1.10設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 6),則存在1-正則且最優(yōu)(4× v,{3,4},1,(6/7,1/7))-OOC.定理1.11設(shè)v為正整數(shù)且u的每個質(zhì)因子p≡1(mod 6),則存在1-正則且最優(yōu)(4 × v,{3,4},1,(10/13,3/13))-OOC.定理1.12設(shè)u為正整數(shù)且v的每個質(zhì)因子p≡1(mod 6),則存在1-正則且最優(yōu)(5 × v,{3,4},1,(3/4,1/4))-OOC.定理1.13設(shè)v為正整數(shù)且v的每個質(zhì)因子p≡1(mod 6),則存在1-正則且最優(yōu)(5 × v,{3,4},1,(19/22,3/22))-OOC.定理1.14設(shè)v為正整數(shù),v的每個質(zhì)因子p≡7(mod 12)且p31,則存在1-正則且最優(yōu)(4 × v,{3,4},1,(6/11,5/11))-OOC.定理1.15設(shè)v為正整數(shù)且u的每個質(zhì)因子p ≡ 1(mod 4),則存在1-正則且最優(yōu)(5 × v,{3,4,5},1,(3/5,1/5,1/5))-OOC.定理1.16如果在Zv上存在斜Starter,則存在1-正則且最優(yōu)(7 × {3,4,5},1,(7/11,3/11,1/11))-OOC.本文共分四章:第一章介紹本文相關(guān)概念及本文的主要結(jié)果,第二章給出最優(yōu)(u×u,{3,4}.1,Q)-OOCs的構(gòu)造,第三章給出最優(yōu)(u × v,{3,4,5},1,Q)-OOCs的構(gòu)造,第四章是小結(jié)及可進(jìn)一步研究的問題.
[Abstract]:In 1989, Salehi proposed the concept of one dimensional One-Dimensional Constant-Weight Op-tical Orthogonal Code (1D CWOOC), which was used as a signature sequence in the optical code division multiple access (OCDMA) system. One-Dimensional Variable-Weight Optical Orthogonal Code (1D VWOOC) is used for OCDMA systems. With the rapid development of the society, the demand for different types of information is gradually improved. This requires the production of high speed, large capacity, and different bit error rate OCDMA systems. In order to extend the optical orthogonal code, Yang is proposed in 1997. Two dimensional constant weight optical orthogonal codes (Two-Dimensional Constant-Weight Optical Orthogonal Code, 2D CWOOC) are given, but similar to one dimensional constant weight optical orthogonal codes, two dimensional constant weight optical orthogonal codes can only meet single quality service requirements. In order to solve this problem, Yang introduced a two-dimensional variable weight optical orthogonal code (Two-Dimensional) in 2001. Variable-Weight Optical Orthogonal Code, 2D VWOOC). Below the definition of two-dimensional variable weight optical orthogonal codes. Set W ={w1, W2, and wr} are positive integer sets, and a = (lambda a (1), lambda a (2)) as positive integer array. The weight optical orthogonal code or (U * V, W, a, C, Q) -OOC C, which is a cluster of U * V (0,1) matrix (codeword), and satisfies the following three properties: (1) the code word weight distribution: the Hamming weight of the codeword in the C is all in the set, and 1 is less than equal or equal to the number of total codewords. 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Obviously, it is = (1). So, the constant weight is considered to be an optical orthogonal code, when its number of codes reaches the maximum value, it is called optimal. The structure of the optimal (U * V, W, 1, Q) -OOC has some achievements, but there is not much existence of the existence of the optimal two-dimensional variable weight optical orthogonal codes known by the author. This paper will continue to study and obtain the following main results. Theorem 1.1 there is a 1- regular and optimal (6 x V, {3,4}, 1, (4/5,1/5)) -O if there is a skew Starter on Zv. OC. theorem 1.2 if there is a skew Starter on Zv, there is a 1- regular (6 x V, {3,4}, 1, (2/3,1/3)) -OOC. theorem 1.3 if there is a skew Starter in Zv, then there exists a 1- regular (9 * V, 1, 1) theorem 1.4 for every qualitative factor 1. 1.5 set V as positive integer and each qualitative factor of V (MOD 4), there is a 1- regular and optimal (6 x V, {3,4}, 1, (6/7,1/7)) -OOC. theorem 1.6 to set V as positive integer and V for every qualitative factor p 1 (4). 1- regular and optimal (6 * V, {3,4}, 1, (22/23,1/23)) -OOC. theorem 1.8 set V as positive integer and every qualitative factor p of v 1 (MOD 6), then there exists 1- regular and optimal (6 * V, {3,4}, 1,) 1.9 for every qualitative factor 1 (6). Positive integers and every qualitative factor of V (MOD 6), there is a 1- regular and optimal (4 * V, {3,4}, 1, (6/7,1/7)) -OOC. theorem 1.11 to set V as a positive integer and u for every qualitative factor p 1 (MOD 6), then there exists a regular and optimal (4 x, 1, 1) theorem 1.12 with a positive integer and every qualitative factor 1 (6), and there is a regular regularity. And the optimal (5 x V, {3,4}, 1, (3/4,1/4)) -OOC. theorem 1.13 set V as a positive integer and every qualitative factor of V P 1 (MOD 6), then there is a 1- regular and optimal (5 * V, {3,4}, 1, (19/22,3/22)) theorem 1.14. V is a positive integer and every qualitative factor of u p 1 (MOD 4), there is a 1- regular and optimal (5 x V, {3,4,5}, 1, (3/5,1/5,1/5)) -OOC. theorem 1.16 if there is a Starter Starter on Zv, then there are 1- canonical and optimal (7 x 1, (1)) altogether four chapters: the first chapter introduces the relevant concepts and the main results of this article, first chapter The two chapter gives the structure of the optimal (U * u, {3,4}.1, Q) -OOCs, and the third chapter gives the construction of the optimal (U * V, {3,4,5}, 1, Q) -OOCs. The fourth chapter is a summary and further research.

【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.4

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本文編號：1888589