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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. Google Scholar 
[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. Google Scholar 
[3] 
P. Z. Fan, W. N. Yuan and Y. F. Tu, Zcomplementary binary sequences,, IEEE Signal Process. Lett., 14 (2007), 509. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[7] 
M. J. E. Golay, Complementary series,, IRE. Trans. Inf. Theory, 7 (1961), 82. Google Scholar 
[8] 
T. Hayashi, Ternary sequence set having periodic and aperiodic zerocorrelation zone,, IEICE Trans. Fundamentals, E89A (2006), 1825. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[17] 
X. D. Li, P. Z. Fan, X. H. Tang and L. Hao, Quadriphase Zcomplementary sequences,, IEICE Trans. Fundamentals, E93A (2010), 2251. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[20] 
K. Omata, H. Torii and T. Matsumoto, Zerocrosscorrelation properties of asymmetric ZCZ sequence sets,, IEICE Trans. Fundamentals, E95A (2012), 1926. Google Scholar 
[21] 
A. Rathinakumar and A. K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences,, Electron. Lett., 40 (2004), 1133. Google Scholar 
[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. Google Scholar 
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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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[27] 
H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric ZCZ sequences sets,, IEICE Trans. Fundamentals, E95A (2012), 1577. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[33] 
F. X. Zeng, New perfect ployphase sequences and mutually orthogonal ZCZ polyphase sequence sets,, IEICE trans. Fundamentals, E92A (2009), 1731. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
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. Google Scholar 
[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. Google Scholar 
[3] 
P. Z. Fan, W. N. Yuan and Y. F. Tu, Zcomplementary binary sequences,, IEEE Signal Process. Lett., 14 (2007), 509. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[7] 
M. J. E. Golay, Complementary series,, IRE. Trans. Inf. Theory, 7 (1961), 82. Google Scholar 
[8] 
T. Hayashi, Ternary sequence set having periodic and aperiodic zerocorrelation zone,, IEICE Trans. Fundamentals, E89A (2006), 1825. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[17] 
X. D. Li, P. Z. Fan, X. H. Tang and L. Hao, Quadriphase Zcomplementary sequences,, IEICE Trans. Fundamentals, E93A (2010), 2251. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[20] 
K. Omata, H. Torii and T. Matsumoto, Zerocrosscorrelation properties of asymmetric ZCZ sequence sets,, IEICE Trans. Fundamentals, E95A (2012), 1926. Google Scholar 
[21] 
A. Rathinakumar and A. K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences,, Electron. Lett., 40 (2004), 1133. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[27] 
H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric ZCZ sequences sets,, IEICE Trans. Fundamentals, E95A (2012), 1577. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[33] 
F. X. Zeng, New perfect ployphase sequences and mutually orthogonal ZCZ polyphase sequence sets,, IEICE trans. Fundamentals, E92A (2009), 1731. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
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