# American Institute of Mathematical Sciences

May  2012, 6(2): 237-247. doi: 10.3934/amc.2012.6.237

## Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping

 1 College of Communication Engineering, Chongqing University, Chongqing 400044, China, and Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035, China 2 College of Communication Engineering, Chongqing University, Chongqing 400044, China 3 Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035, China, China

Received  June 2011 Revised  January 2012 Published  April 2012

A family of quaternary periodic complementary sequence (PCS) or Z-complementary sequence (PZCS) sets is presented. By combining an interleaving technique and the inverse Gray mapping, the proposed method transforms the known binary PCS/PZCS sets with odd length of sub-sequences into quaternary PCS/PZCS sets, but the length of new sub-sequences is twice as long as that of the original sub-sequences, which is a drawback of this proposed method. However, the shortcoming that the method proposed by J. W. Jang, et al. is merely fit for even length of sub-sequences is overcome. As a consequence, the union of our and J. W. Jang, et al.'s methods allows us to construct quaternary PCS/PZCS sets from binary PCS/PZCS sets with sub-sequences of arbitrary length.
Citation: Fanxin Zeng, Xiaoping Zeng, Zhenyu Zhang, Guixin Xuan. Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping. Advances in Mathematics of Communications, 2012, 6 (2) : 237-247. doi: 10.3934/amc.2012.6.237
##### References:

show all references

##### References:
 [1] Ji-Woong Jang, Young-Sik Kim, Sang-Hyo Kim, Dae-Woon Lim. New construction methods of quaternary periodic complementary sequence sets. Advances in Mathematics of Communications, 2010, 4 (1) : 61-68. doi: 10.3934/amc.2010.4.61 [2] Yang Yang, Xiaohu Tang, Guang Gong. Even periodic and odd periodic complementary sequence pairs from generalized Boolean functions. Advances in Mathematics of Communications, 2013, 7 (2) : 113-125. doi: 10.3934/amc.2013.7.113 [3] Zhenyu Zhang, Lijia Ge, Fanxin Zeng, Guixin Xuan. Zero correlation zone sequence set with inter-group orthogonal and inter-subgroup complementary properties. Advances in Mathematics of Communications, 2015, 9 (1) : 9-21. doi: 10.3934/amc.2015.9.9 [4] Liqun Yao, Wenli Ren, Yong Wang, Chunming Tang. Z-complementary pairs with flexible lengths and large zero odd-periodic correlation zones. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021037 [5] Ji-Woong Jang, Young-Sik Kim, Sang-Hyo Kim. New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set. Advances in Mathematics of Communications, 2009, 3 (2) : 115-124. doi: 10.3934/amc.2009.3.115 [6] Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237-244. doi: 10.3934/amc.2017015 [7] Yixiao Qiao, Xiaoyao Zhou. Zero sequence entropy and entropy dimension. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 435-448. doi: 10.3934/dcds.2017018 [8] Walter Briec, Bernardin Solonandrasana. Some remarks on a successive projection sequence. Journal of Industrial & Management Optimization, 2006, 2 (4) : 451-466. doi: 10.3934/jimo.2006.2.451 [9] Huaning Liu, Xi Liu. On the correlation measures of orders $3$ and $4$ of binary sequence of period $p^2$ derived from Fermat quotients. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021008 [10] Yuhua Sun, Zilong Wang, Hui Li, Tongjiang Yan. The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$. Advances in Mathematics of Communications, 2013, 7 (4) : 409-424. doi: 10.3934/amc.2013.7.409 [11] Tinghua Hu, Yang Yang, Zhengchun Zhou. Golay complementary sets with large zero odd-periodic correlation zones. Advances in Mathematics of Communications, 2021, 15 (1) : 23-33. doi: 10.3934/amc.2020040 [12] Longye Wang, Gaoyuan Zhang, Hong Wen, Xiaoli Zeng. An asymmetric ZCZ sequence set with inter-subset uncorrelated property and flexible ZCZ length. Advances in Mathematics of Communications, 2018, 12 (3) : 541-552. doi: 10.3934/amc.2018032 [13] Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135 [14] Matthew Macauley, Henning S. Mortveit. Update sequence stability in graph dynamical systems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1533-1541. doi: 10.3934/dcdss.2011.4.1533 [15] Wenjun Xia, Jinzhi Lei. Formulation of the protein synthesis rate with sequence information. Mathematical Biosciences & Engineering, 2018, 15 (2) : 507-522. doi: 10.3934/mbe.2018023 [16] Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 3017-3025. doi: 10.3934/dcdss.2020465 [17] Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $\beta$-transformation. Discrete & Continuous Dynamical Systems, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267 [18] Finley Freibert. The classification of complementary information set codes of lengths $14$ and $16$. Advances in Mathematics of Communications, 2013, 7 (3) : 267-278. doi: 10.3934/amc.2013.7.267 [19] Wenbing Chen, Jinquan Luo, Yuansheng Tang, Quanquan Liu. Some new results on cross correlation of $p$-ary $m$-sequence and its decimated sequence. Advances in Mathematics of Communications, 2015, 9 (3) : 375-390. doi: 10.3934/amc.2015.9.375 [20] Hua Liang, Jinquan Luo, Yuansheng Tang. On cross-correlation of a binary $m$-sequence of period $2^{2k}-1$ and its decimated sequences by $(2^{lk}+1)/(2^l+1)$. Advances in Mathematics of Communications, 2017, 11 (4) : 693-703. doi: 10.3934/amc.2017050

2020 Impact Factor: 0.935