
Previous Article
Existence conditions for selforthogonal negacyclic codes over finite fields
 AMC Home
 This Issue

Next Article
Some new classes of cyclic codes with three or six weights
Zero correlation zone sequence set with intergroup orthogonal and intersubgroup complementary properties
1.  College of Communication Engineering, Chongqing University, Chongqing 400044, China, China 
2.  College of Communication Engineering, Chongqing University, Chongqing 400044, China, and Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035 
3.  Chongqing Key Laboratory of Emergency Communication, Chongqing Communication Institute, Chongqing 400035 
References:
[1] 
H. H. Chen, Y. C. Yeh, et al., Generalized pairwise complementary codes with setwise uniform interferencefree windows,, IEEE J. Sel. Areas Commun., 24 (2006), 65. 
[2] 
P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. M. Deng, A class of binary sequences with zero correlation zone,, Electr. Lett., 35 (1999), 777. 
[3] 
P. Z. Fan, W. N. Yuan and Y. F. Tu, Zcomplementary binary sequences,, IEEE Signal Process. Lett., 14 (2007), 509. 
[4] 
L. F. Feng, P. Z. Fan, X. H. Tang and K.K. Loo, Generalized pairwise Zcomplementary codes,, IEEE Signal Process. Lett., 15 (2008), 377. 
[5] 
L. F. Feng, X. W. Zhou and P. Z. Fan, A construction of intergroup complementary codes with flexible ZCZ length,, J. Zhejiang Univ. Sci. C, 12 (2011), 846. 
[6] 
L. F. Feng, X. W. Zhou and X. Y. Li, A general construction of intergroup complementary codes based on Zcomplementary codes and perfect periodic crosscorrelation codes,, Wireless Pers. Commun., 71 (2012), 695. 
[7] 
M. J. E. Golay, Complementary series,, IRE. Trans. Inf. Theory, 7 (1961), 82. 
[8] 
T. Hayashi, Ternary sequence set having periodic and aperiodic zerocorrelation zone,, IEICE Trans. Fundamentals, E89A (2006), 1825. 
[9] 
T. Hayashi, T. Maeda and S. Matsufuji, A generalized construction scheme of a zerocorrelation zone sequence set with a wide intersubset zerocorrelation zone,, IEICE Trans. Fundamentals, E95A (2012), 1931. 
[10] 
T. Hayashi, T. Maeda, S. Matsufuji and S. Okawa, A ternary zerocorrelation zone sequence set having wide intersubset zerocorrelation zone,, IEICE Trans. Fundamentals, E94A (2011), 2230. 
[11] 
T. Hayashi, T. Maeda and S. Okawa, A generalized construction of zerocorrelation zone sequence set with sequence subsets,, IEICE Trans. Fundamentals, E94A (2011), 1597. 
[12] 
T. Hayashi and S. Matsufuji, A generalized construction of optimal zerocorrelation zone sequence set from a perfect sequence pair,, IEICE Trans. Fundamentals, E93A (2010), 2337. 
[13] 
H. G. Hu and G. Gong, New sets of zero or low correlation zone sequences via interleaving techniques,, IEEE Trans. Inf. Theory, 56 (2010), 1702. doi: 10.1109/TIT.2010.2040887. 
[14] 
J. W. Jang, Y. S. Kim and S. H. Kim, New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set,, Adv. Math. Commun., 3 (2009), 115. doi: 10.3934/amc.2009.3.115. 
[15] 
J. W. Jang, Y. S. Kim, S. H. Kim and D. W. Lim, New construction methods of quaternary periodic complementary sequence sets,, Adv. Math. Commun., 4 (2010), 61. doi: 10.3934/amc.2010.4.61. 
[16] 
J. Li, A. P. Huang, M. Guizani and H. H. Chen, Intergroup complementary codes for interferenceresistant CDMA wireless communications,, IEEE Trans. Wireless Commun., 7 (2008), 166. 
[17] 
X. D. Li, P. Z. Fan, X. H. Tang and L. Hao, Quadriphase Zcomplementary sequences,, IEICE Trans. Fundamentals, E93A (2010), 2251. 
[18] 
Y. B. Li, C. Q. Xu and K. Liu, Construction of mutually orthogonal zero correlation zone polyphase sequence sets,, IEICE Trans. Fundamentals, E94A (2011), 1159. 
[19] 
S. Matsufuji, T. Matsumoto, T. Hayashida, T. Hayashi, N. Kuroyanagi and P. Z. FAN, On a ZCZ code including a sequence used for a synchronization symbol,, IEICE Trans. Fundamentals, E93A (2010), 2286. 
[20] 
K. Omata, H. Torii and T. Matsumoto, Zerocrosscorrelation properties of asymmetric ZCZ sequence sets,, IEICE Trans. Fundamentals, E95A (2012), 1926. 
[21] 
A. Rathinakumar and A. K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences,, Electron. Lett., 40 (2004), 1133. 
[22] 
A. Rathinakumar and A. K. Chaturvedi, A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences,, IEEE Trans. Inf. Theory, 52 (2006), 3817. doi: 10.1109/TIT.2006.878171. 
[23] 
A. Rathinakumar and A. K. Chaturvedi, Complete mutually orthogonal Golay complementary sets from ReedMuller codes,, IEEE Trans. Inf. Theory, 54 (2008), 1339. doi: 10.1109/TIT.2007.915980. 
[24] 
X. H. Tang, P. Z. Fan and J. Lindner, Multiple binary ZCZ sequence sets with good crosscorrelation property based on complementary sequence sets,, IEEE Trans. Inf. Theory, 56 (2010), 4038. doi: 10.1109/TIT.2010.2050796. 
[25] 
X. H. Tang and W. H. Mow, Design of spreading codes for quasisynchronous CDMA with intercell interference,, IEEE J. Sel. Areas Commun., 24 (2006), 84. 
[26] 
X. H. Tang and W. H. Mow, A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences,, IEEE Trans. Inf. Theory, 54 (2008), 5729. doi: 10.1109/TIT.2008.2006574. 
[27] 
H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric ZCZ sequences sets,, IEICE Trans. Fundamentals, E95A (2012), 1577. 
[28] 
H. Torii, M. Nakamura and N. Suehiro, A new class of zerocorrelation zone sequences,, IEEE Trans. Inf. Theory, 50 (2004), 559. doi: 10.1109/TIT.2004.825399. 
[29] 
H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Generalized mutually orthogonal ZCZ sequence sets based on perfect sequences and orthogonal codes,, in Proc. 15th Int. Conf. Adv. Commun. Techn., (2013), 894. 
[30] 
H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Quasioptimal and optimal generalized mutually orthogonal ZCZ sequence sets based on an interleaving technique,, Int. J. Commun., 7 (2013), 18. 
[31] 
Y. F. Tu, P. Z. Fan, L. Hao and X. Y. Li, Construction of binary array set with zero correlation zone based on interleaving technique,, IEICE Trans. Fundamentals, E94A (2011), 766. doi: 10.1587/transfun.E94.A.766. 
[32] 
Y. F. Tu, P. Z. Fan, L. Hao and X. H. Tang, A simple method for generating optimal Zperiodic complementary sequence set based on phase shift,, IEEE Signal Process. Lett., 17 (2010), 891. 
[33] 
F. X. Zeng, New perfect ployphase sequences and mutually orthogonal ZCZ polyphase sequence sets,, IEICE trans. Fundamentals, E92A (2009), 1731. 
[34] 
F. X. Zeng, X. P. Zeng, Z. Y. Zhang and G. X. Xuan, Quaternary periodic complementary/Zcomplementary sequence sets based upon interleaving technique and Gray mapping,, Adv. Math. Commun., 6 (2012), 237. doi: 10.3934/amc.2012.6.237. 
[35] 
C. Zhang, X. M. Tao, S. Yamada and M. Hatori, Sequence set with three zero correlation zone and its application in MCCDMA system,, IEICE Trans. Fundamentals, E89A (2006), 2275. doi: 10.1093/ietfec/e89a.9.2275. 
[36] 
Z. Y. Zhang, W. Chen, F. X. Zeng, H. Wu and Y. H. Zhong, Zcomplementary sets based on sequences with periodic and aperiodic zero correlation zone,, EURASIP J. Wireless Comm. Networking, 2009 (2009), 1. doi: 10.1155/2009/418026. 
[37] 
Z. Y. Zhang, F. X. Zeng and G. X. Xuan, A class of complementary sequences with multiwidth zero crosscorrelation zone,, IEICE Trans. Fundamentals, E93A (2010), 1508. doi: 10.1587/transfun.E93.A.1508. 
[38] 
Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique,, IEEE Trans. Inf. Theory, 54 (2008), 4267. doi: 10.1109/TIT.2008.928256. 
show all references
References:
[1] 
H. H. Chen, Y. C. Yeh, et al., Generalized pairwise complementary codes with setwise uniform interferencefree windows,, IEEE J. Sel. Areas Commun., 24 (2006), 65. 
[2] 
P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. M. Deng, A class of binary sequences with zero correlation zone,, Electr. Lett., 35 (1999), 777. 
[3] 
P. Z. Fan, W. N. Yuan and Y. F. Tu, Zcomplementary binary sequences,, IEEE Signal Process. Lett., 14 (2007), 509. 
[4] 
L. F. Feng, P. Z. Fan, X. H. Tang and K.K. Loo, Generalized pairwise Zcomplementary codes,, IEEE Signal Process. Lett., 15 (2008), 377. 
[5] 
L. F. Feng, X. W. Zhou and P. Z. Fan, A construction of intergroup complementary codes with flexible ZCZ length,, J. Zhejiang Univ. Sci. C, 12 (2011), 846. 
[6] 
L. F. Feng, X. W. Zhou and X. Y. Li, A general construction of intergroup complementary codes based on Zcomplementary codes and perfect periodic crosscorrelation codes,, Wireless Pers. Commun., 71 (2012), 695. 
[7] 
M. J. E. Golay, Complementary series,, IRE. Trans. Inf. Theory, 7 (1961), 82. 
[8] 
T. Hayashi, Ternary sequence set having periodic and aperiodic zerocorrelation zone,, IEICE Trans. Fundamentals, E89A (2006), 1825. 
[9] 
T. Hayashi, T. Maeda and S. Matsufuji, A generalized construction scheme of a zerocorrelation zone sequence set with a wide intersubset zerocorrelation zone,, IEICE Trans. Fundamentals, E95A (2012), 1931. 
[10] 
T. Hayashi, T. Maeda, S. Matsufuji and S. Okawa, A ternary zerocorrelation zone sequence set having wide intersubset zerocorrelation zone,, IEICE Trans. Fundamentals, E94A (2011), 2230. 
[11] 
T. Hayashi, T. Maeda and S. Okawa, A generalized construction of zerocorrelation zone sequence set with sequence subsets,, IEICE Trans. Fundamentals, E94A (2011), 1597. 
[12] 
T. Hayashi and S. Matsufuji, A generalized construction of optimal zerocorrelation zone sequence set from a perfect sequence pair,, IEICE Trans. Fundamentals, E93A (2010), 2337. 
[13] 
H. G. Hu and G. Gong, New sets of zero or low correlation zone sequences via interleaving techniques,, IEEE Trans. Inf. Theory, 56 (2010), 1702. doi: 10.1109/TIT.2010.2040887. 
[14] 
J. W. Jang, Y. S. Kim and S. H. Kim, New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set,, Adv. Math. Commun., 3 (2009), 115. doi: 10.3934/amc.2009.3.115. 
[15] 
J. W. Jang, Y. S. Kim, S. H. Kim and D. W. Lim, New construction methods of quaternary periodic complementary sequence sets,, Adv. Math. Commun., 4 (2010), 61. doi: 10.3934/amc.2010.4.61. 
[16] 
J. Li, A. P. Huang, M. Guizani and H. H. Chen, Intergroup complementary codes for interferenceresistant CDMA wireless communications,, IEEE Trans. Wireless Commun., 7 (2008), 166. 
[17] 
X. D. Li, P. Z. Fan, X. H. Tang and L. Hao, Quadriphase Zcomplementary sequences,, IEICE Trans. Fundamentals, E93A (2010), 2251. 
[18] 
Y. B. Li, C. Q. Xu and K. Liu, Construction of mutually orthogonal zero correlation zone polyphase sequence sets,, IEICE Trans. Fundamentals, E94A (2011), 1159. 
[19] 
S. Matsufuji, T. Matsumoto, T. Hayashida, T. Hayashi, N. Kuroyanagi and P. Z. FAN, On a ZCZ code including a sequence used for a synchronization symbol,, IEICE Trans. Fundamentals, E93A (2010), 2286. 
[20] 
K. Omata, H. Torii and T. Matsumoto, Zerocrosscorrelation properties of asymmetric ZCZ sequence sets,, IEICE Trans. Fundamentals, E95A (2012), 1926. 
[21] 
A. Rathinakumar and A. K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences,, Electron. Lett., 40 (2004), 1133. 
[22] 
A. Rathinakumar and A. K. Chaturvedi, A new framework for constructing mutually orthogonal complementary sets and ZCZ sequences,, IEEE Trans. Inf. Theory, 52 (2006), 3817. doi: 10.1109/TIT.2006.878171. 
[23] 
A. Rathinakumar and A. K. Chaturvedi, Complete mutually orthogonal Golay complementary sets from ReedMuller codes,, IEEE Trans. Inf. Theory, 54 (2008), 1339. doi: 10.1109/TIT.2007.915980. 
[24] 
X. H. Tang, P. Z. Fan and J. Lindner, Multiple binary ZCZ sequence sets with good crosscorrelation property based on complementary sequence sets,, IEEE Trans. Inf. Theory, 56 (2010), 4038. doi: 10.1109/TIT.2010.2050796. 
[25] 
X. H. Tang and W. H. Mow, Design of spreading codes for quasisynchronous CDMA with intercell interference,, IEEE J. Sel. Areas Commun., 24 (2006), 84. 
[26] 
X. H. Tang and W. H. Mow, A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences,, IEEE Trans. Inf. Theory, 54 (2008), 5729. doi: 10.1109/TIT.2008.2006574. 
[27] 
H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric ZCZ sequences sets,, IEICE Trans. Fundamentals, E95A (2012), 1577. 
[28] 
H. Torii, M. Nakamura and N. Suehiro, A new class of zerocorrelation zone sequences,, IEEE Trans. Inf. Theory, 50 (2004), 559. doi: 10.1109/TIT.2004.825399. 
[29] 
H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Generalized mutually orthogonal ZCZ sequence sets based on perfect sequences and orthogonal codes,, in Proc. 15th Int. Conf. Adv. Commun. Techn., (2013), 894. 
[30] 
H. Torii, M. Satoh, T. Matsumoto and M. Nakamura, Quasioptimal and optimal generalized mutually orthogonal ZCZ sequence sets based on an interleaving technique,, Int. J. Commun., 7 (2013), 18. 
[31] 
Y. F. Tu, P. Z. Fan, L. Hao and X. Y. Li, Construction of binary array set with zero correlation zone based on interleaving technique,, IEICE Trans. Fundamentals, E94A (2011), 766. doi: 10.1587/transfun.E94.A.766. 
[32] 
Y. F. Tu, P. Z. Fan, L. Hao and X. H. Tang, A simple method for generating optimal Zperiodic complementary sequence set based on phase shift,, IEEE Signal Process. Lett., 17 (2010), 891. 
[33] 
F. X. Zeng, New perfect ployphase sequences and mutually orthogonal ZCZ polyphase sequence sets,, IEICE trans. Fundamentals, E92A (2009), 1731. 
[34] 
F. X. Zeng, X. P. Zeng, Z. Y. Zhang and G. X. Xuan, Quaternary periodic complementary/Zcomplementary sequence sets based upon interleaving technique and Gray mapping,, Adv. Math. Commun., 6 (2012), 237. doi: 10.3934/amc.2012.6.237. 
[35] 
C. Zhang, X. M. Tao, S. Yamada and M. Hatori, Sequence set with three zero correlation zone and its application in MCCDMA system,, IEICE Trans. Fundamentals, E89A (2006), 2275. doi: 10.1093/ietfec/e89a.9.2275. 
[36] 
Z. Y. Zhang, W. Chen, F. X. Zeng, H. Wu and Y. H. Zhong, Zcomplementary sets based on sequences with periodic and aperiodic zero correlation zone,, EURASIP J. Wireless Comm. Networking, 2009 (2009), 1. doi: 10.1155/2009/418026. 
[37] 
Z. Y. Zhang, F. X. Zeng and G. X. Xuan, A class of complementary sequences with multiwidth zero crosscorrelation zone,, IEICE Trans. Fundamentals, E93A (2010), 1508. doi: 10.1587/transfun.E93.A.1508. 
[38] 
Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique,, IEEE Trans. Inf. Theory, 54 (2008), 4267. doi: 10.1109/TIT.2008.928256. 
[1] 
JiWoong Jang, YoungSik Kim, SangHyo Kim, DaeWoon Lim. New construction methods of quaternary periodic complementary sequence sets. Advances in Mathematics of Communications, 2010, 4 (1) : 6168. doi: 10.3934/amc.2010.4.61 
[2] 
Fanxin Zeng, Xiaoping Zeng, Zhenyu Zhang, Guixin Xuan. Quaternary periodic complementary/Zcomplementary sequence sets based on interleaving technique and Gray mapping. Advances in Mathematics of Communications, 2012, 6 (2) : 237247. doi: 10.3934/amc.2012.6.237 
[3] 
Longye Wang, Gaoyuan Zhang, Hong Wen, Xiaoli Zeng. An asymmetric ZCZ sequence set with intersubset uncorrelated property and flexible ZCZ length. Advances in Mathematics of Communications, 2018, 12 (3) : 541552. doi: 10.3934/amc.2018032 
[4] 
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) : 113125. doi: 10.3934/amc.2013.7.113 
[5] 
Yixiao Qiao, Xiaoyao Zhou. Zero sequence entropy and entropy dimension. Discrete & Continuous Dynamical Systems  A, 2017, 37 (1) : 435448. doi: 10.3934/dcds.2017018 
[6] 
Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal lowhitzone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 6779. doi: 10.3934/amc.2018004 
[7] 
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) : 375390. doi: 10.3934/amc.2015.9.375 
[8] 
Zilong Wang, Guang Gong. Correlation of binary sequence families derived from the multiplicative characters of finite fields. Advances in Mathematics of Communications, 2013, 7 (4) : 475484. doi: 10.3934/amc.2013.7.475 
[9] 
Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequencyhopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 5562. doi: 10.3934/amc.2015.9.55 
[10] 
Hua Liang, Wenbing Chen, Jinquan Luo, Yuansheng Tang. A new nonbinary sequence family with low correlation and large size. Advances in Mathematics of Communications, 2017, 11 (4) : 671691. doi: 10.3934/amc.2017049 
[11] 
Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237244. doi: 10.3934/amc.2017015 
[12] 
Xiaohui Liu, Jinhua Wang, Dianhua Wu. Two new classes of binary sequence pairs with threelevel crosscorrelation. Advances in Mathematics of Communications, 2015, 9 (1) : 117128. doi: 10.3934/amc.2015.9.117 
[13] 
Walter Briec, Bernardin Solonandrasana. Some remarks on a successive projection sequence. Journal of Industrial & Management Optimization, 2006, 2 (4) : 451466. doi: 10.3934/jimo.2006.2.451 
[14] 
Yuhua Sun, Zilong Wang, Hui Li, Tongjiang Yan. The crosscorrelation 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) : 409424. doi: 10.3934/amc.2013.7.409 
[15] 
Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zerosum linearquadratic differential game: Saddlepoint equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 120. doi: 10.3934/naco.2017001 
[16] 
KaiUwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135156. doi: 10.3934/amc.2009.3.135 
[17] 
Matthew Macauley, Henning S. Mortveit. Update sequence stability in graph dynamical systems. Discrete & Continuous Dynamical Systems  S, 2011, 4 (6) : 15331541. doi: 10.3934/dcdss.2011.4.1533 
[18] 
Wenjun Xia, Jinzhi Lei. Formulation of the protein synthesis rate with sequence information. Mathematical Biosciences & Engineering, 2018, 15 (2) : 507522. doi: 10.3934/mbe.2018023 
[19] 
JiWoong Jang, YoungSik Kim, SangHyo 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) : 115124. doi: 10.3934/amc.2009.3.115 
[20] 
Hua Liang, Jinquan Luo, Yuansheng Tang. On crosscorrelation 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) : 693703. doi: 10.3934/amc.2017050 
2017 Impact Factor: 0.564
Tools
Metrics
Other articles
by authors
[Back to Top]