码重为3和7的最优光正交码的具体构造

Explicit Constructions of Optimal Optical Orthogonal Code with Weights 3 and 7

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.

Constructing optical orthogonal codes （OOC） cause for many researchers concern because it has many applications in the optical code division multiple access （OCDMA） net- work. So far, much works have been devoted to optimal variable-weight （n, W, 1, Q）-OOC with W e {{3, 4}, {3, 5}, {3, 6}, {4, 5}, {4, 6}}. However, explicit constructions of optimal （n, W, 1, Q）-OOC with W = {3, 7} are very few. In this paper, an infinite class of explicit constructions of new optimal variable-weight （33p, {3, 7}, 1, {4/5,1/5））-OOC are presented, for any prime p ---- 3 （mod 4） and p 〉 7.