两类新的最优变重量光正交码

变重量光正交码用于光码分多址通信系统以满足不同服务质量用户需求.给出当u≥5为素数时,最优(16u,{3,5},1,{2/3,1/3))交重量光正交码的具体构造.同时证明了当u≥5为素数时,存在一个最优(25u,{3,4,5},1,{1/4,2/4,1/4})变重量光正交码.这将改进变重量光正交码的存在性结果.     

码重为3和7的最优光正交码的具体构造

对光正交码(OOC)构造的关注源于它在光码分多址网络中有许多应用.截至目前,对于码重为W∈{{3,4},{3,5},{3,6},{4,5},{4,6]}的变重量光正交码的构造已经取得许多结果.然而,对于码重为W={3,7}的变重量光正交码的具体构造非常的少.给出一系列新的最优变重量光正交码(33p,{3,7},1,{4/5,1/5})-OOC的具体构造,对于任何素数p≡3(mod 4)且p≥7.     

参数为(W,1,Q;v)的循环填充与最优变重量光正交码（英文）

为了满足多媒体光码分多址多种不同的服务质量要求,杨谷章引入了变重量光正交码.对于码重W={3,4},{3,7},{4,7},{3,4,7},本文通过循环填充构造出一系列参数为(v,W,1,Q)变重量光正交码.     

超单严格循环设计的一些结果

主要研究基于(v,k,2)光正交码的最优超单严格循环填充,即(v,k,λ)-OSCP的存在性问题,解决了λ=2,3,4的(v,3,λ)-OSCP的存在性,得到了一些k≥4的(v,k,λ)-OSCP的无穷类.     

一类最优光正交码的组合构作

光正交码具有良好的光学相关特性, 它特别适用于光纤信道上的码分多址系统. 利用Weil定理给出了参数为(15p , 5,1)的最优光正交码的组合构作, 其中p为模4余1且大于5的素数. 由此, 当正整数v 的质因子均为模4余1且大于5的素数时, (15v, 5,1)最优光正交码可利用已知的递归构造方法得到.     

一种OLS/OOC二维光正交码的构造与性能分析

利用不同的序列作为波长跳频序列和时间扩频序列可以构造出不同的二维光正交码在众多文献中已有所报道.在经过正交拉丁方(OLS)与跳频序列的相关性研究之后.做了以下主要工作:首先,将正交拉丁方(OLS)序列作为波长跳频序列,结合一维时间扩频序列(OOC),构造了一种OLS/OOC二维光正交码.然后,本文对构造的OLS/OOC进行了多种性能仿真和分析.相对于PC/OOC、OCFHC/OOC等二维光正交码而言,OLS/OOC的波长数并不局限于素数,更能充分利用MWOCDMA系统中的有效波长数.仿真和分析表明:码字具有很好的相关性能,码字容量直逼理论极限,为一种渐近最优二维光正交码.     

(Z_u×Z_v,4,1)差填充及其在光正交签名码中的应用（英）

为了解决二维图像的并行传输,北山研一引入了光正交签名码.在光正交签名码的研究中,(Z_u×Z_v,k,1)差填充起到重要的作用.本文给出了群Z_3×Z_(gp)上(3×gp,3×g,4,1)-DF和群Z_(3p)×Z_(gp)上(3p×gp,3×g,4,1)-DF的具体构造,其中g=3,6,从而通过递推构造给出若干类最优(Z_u×Z_v,4,1)差填充.因此,我们得到若干类重量为4的光正交签名码.     

几类最优避免冲突码

长度为n重量为w的避免冲突码C是群Z_n的w元子集族,满足对任意的x,y∈C,x≠y有d*(x)∩d*(y)=Φ,其中d*(x)={a-b(mod n):a,b∈x,a≠b}.避免冲突码适用于无反馈时隙同步多址冲突信道.C中的元素称为码字,C中所包含的码字的个数称为码的容量,它是系统中所支持的潜在用户的个数.利用已有的3种构造方法给出了重量在4到10之间的一些最优CAC(p,w)码类.     

重量为3的2q周期强避免冲突中心码的容量

强避免冲突码适用于无反馈异步多址冲突信道.码中所包含的码字的个数称为码的容量,它是系统中所支持的潜在用户的个数.给出了重量ω=3,长度为2q的最优码的构造方法及其容量.     

两类子域码的重量分布（英文）

子域码是一类特殊的线性码.线性码由于其有效的编码及译码算法,在电子消费产品、数据存储系统和通信系统中有广泛的应用.然而,确定线性码的重量分布通常是困难的工作.本文给出了两类二元子域码C₍₍H(f)_<sub>1))~((2))和C₍₍H(f)_<sub>2))~((2))及其对偶码的重量分布,其中f₁(x)=x~4,f₂(x)=x~6+x~4+x~2.     

Optimal (v, 4, 2, 1) optical orthogonal codes with small parameters

Optimal (v, 4,2,1) optical orthogonal codes (OOCs) with v ? 75 and v ≠ 71 are classified up to isomorphism. One (v, 4,2,1) OOC is presented for all v ? 181 , for which an optimal OOC exists. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 20:142‐160, 2012     

Spreads, arcs, and multiple wavelength codes

We present several new families of multiple wavelength (2-dimensional) optical orthogonal codes (2D-OOCs) with ideal auto-correlation λ_a=0 (codes with at most one pulse per wavelength). We also provide a construction which yields multiple weight codes. All of our constructions produce codes that are either optimal with respect to the Johnson bound (J-optimal), or are asymptotically optimal and maximal. The constructions are based on certain pointsets in finite projective spaces of dimension k over GF(q) denoted PG(k,q).     

最优(24u,{3,4},1,{2/3,1/3})光正交码

Variable-weight optical orthogonal codes(OOCs) were introduced by G. C. YANG for multimedia optical CDMA systems with multiple quality of service(Qo S) requirements. In this paper, some infinite classes of optimal cyclic packing are presented. Optimal(24u, {3, 4}, 1,{2/3, 1/3})-OOCs for any positive integer u > 1 are established.     

Bounds and Constructions on (v, 4, 3, 2) Optical Orthogonal Codes

In this paper, we are concerned about optimal (v, 4, 3, 2)‐OOCs. A tight upper bound on the exact number of codewords of optimal (v, 4, 3, 2)‐OOCs and some direct and recursive constructions of optimal (v, 4, 3, 2)‐OOCs are given. As a result, the exact number of codewords of an optimal (v, 4, 3, 2)‐OOC is determined for some infinite series.     

Constructions of optimal variable‐weight optical orthogonal codes

Variable‐weight optical orthogonal code (OOC) was introduced by G‐C Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this article, new infinite classes of optimal (u, W, 1, {1/2, 1/2})‐OOCs are obtained for W={3, 4}, {3, 5} and {3, 6}. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 274–291, 2010     

Bounds and Constructions for Two‐Dimensional Variable‐Weight Optical Orthogonal Codes

Optical orthogonal codes (1D constant‐weight OOCs or 1D CWOOCs) were first introduced by Salehi as signature sequences to facilitate multiple access in optical fibre networks. In fiber optic communications, a principal drawback of 1D CWOOCs is that large bandwidth expansion is required if a big number of codewords is needed. To overcome this problem, a two‐dimensional (2D) (constant‐weight) coding was introduced. Many optimal 2D CWOOCs were obtained recently. A 2D CWOOC can only support a single QoS (quality of service) class. A 2D variable‐weight OOC (2D VWOOC) was introduced to meet multiple QoS requirements. A 2D VWOOC is a set of 0, 1 matrices with variable weight, good auto, and cross‐correlations. Little is known on the construction of optimal 2D VWOOCs. In this paper, new upper bound on the size of a 2D VWOOC is obtained, and several new infinite classes of optimal 2D VWOOCs are obtained.     

On Balanced Optimal Optical Orthogonal Codes

Variable‐weight optical orthogonal codes (OOCs) were introduced by G.‐C. Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this paper, by using incomplete difference matrices and perfect relative difference families, a balanced ‐OOC is obtained for every positive integer .     

Optimal (4up, 5, 1) optical orthogonal codes

By a (ν, k, 1)‐OOC we mean an optical orthogonal code. In this paper, it is proved that an optimal (4p, 5, 1)‐OOC exists for prime p ≡ 1 (mod 10), and that an optimal (4up, 5, 1)‐OOC exists for u = 2, 3 and prime p ≡ 11 (mod 20). These results are obtained by applying Weil's theorem. © 2004 Wiley Periodicals, Inc.     

Maximum two-dimensional （u × v, 4, 1, 3）-OOCs

Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λa, λc） codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D （u × v, 4, 1, 3）-OOC has been determined.