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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. 
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