# A New Hybrid Prime Code for OCDMA Network Multimedia Applications
## 4 Correlation Results  
The simulations in this section are performed to test the auto- and cross-correlation properties of the proposed HPC family at every synchronized time which is equal to the encoded bit time duration and to the time that represents the code sequence length. Figures 1-7 show the auto-correlation property of the HPC sequences \(C_{01}\), \(C_{43}\), \(C_{71}\), \(C_{110}\), \(C_{141}\), \(C_{163}\), and \(C_{182}\), respectively. The results illustrate that the auto-correlation peak value is equal to \"Four\". Such value represents the number of code words in each code sequence belonging to the HPC family. This value can be increased by increasing the number of code words. It is noted that the side lobe values on both sides of the peak value are limited to either \"ZERO\" or \"ONE\" in all results. These results are better than the results obtained from MPC and OOC families.  
Figure 3: Auto-correlation of \(C_{71}\) sequence, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 2: Auto-correlation of \(C_{43}\) sequence, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 4: Auto-correlation of \(C_{110}\) sequence, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 5: Auto-correlation of \(C_{141}\) sequence, \(P_{1}=5\) and \(P_{2}=7\).  
Figures 8-13 represent the value of the cross-correlation between two code sequences in the same group. It is clear that for every synchronized time referred to the shift number \"24\", the cross-correlation value is \"ZERO\". This achieves perfect orthogonality and zero interference at the receiver side.  
Figure 6: Auto-correlation of \(C_{163}\) sequence, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 7: Auto-correlation of \(C_{182}\) sequence, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 8: Cross-correlation between \(C_{11}\) and \(C_{13}\) sequences in same group, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 9: Cross-correlation between \(C_{40}\) and \(C_{42}\) sequences in same group, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 11: Cross-correlation between \(C_{110}\) and \(C_{112}\) sequences in same group, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 10: Cross-correlation between \(C_{71}\) and \(C_{73}\) sequences in same group, \(P_{1}=5\) and \(P_{2}=7\).  
The cross-correlation property between two code sequences from two different groups are illustrated in Figures 14-19. These results show that the cross-correlation value is \"ZERO\" or \"ONE\" at every synchronized time. If the HPC sequences are applied to the asynchronous OCDMA network, each user can communicate in the network at unique  
Figure 12: Cross-correlation between \(C_{160}\) and \(C_{162}\) sequences in same group, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 13: Cross-correlation between \(C_{191}\) and \(C_{193}\)  
time slots that cause out-of-phase and undesirable correlation values, as shown between each synchronized time.  
Figure 14: Cross-correlation between \(C_{03}\) and \(C_{31}\) sequences from different groups, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 15: Cross-correlation between \(C_{21}\) and \(C_{43}\) sequences from different groups, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 16: Cross-correlation between \(C_{60}\) and \(C_{82}\) sequences from different groups, \(P_{1}=5\) and \(P_{2}=7\).  
Figure 17: Cross-correlation between \(C_{92}\) and \(C_{110}\) sequences from different groups, \(P_{1}=5\) and \(P_{2}=7\).