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A class of quaternary sequences with low correlation
1.  Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, Sichuan 610031, China, China 
2.  Department of Informatics, University of Bergen, N5020 Bergen 
References:
[1] 
S. Boztas, R. Hammons and P. V. Kumar, $4$phase sequences with nearoptimum correlation properties, IEEE Trans. Inf. Theory, 14 (1992), 11011113. doi: 10.1109/18.135649. 
[2] 
S. Boztas and P. V. Kumar, Binary sequences with Goldlike correlation but larger linear span, IEEE Trans. Inf. Theory, 40 (1994), 532537. doi: 10.1109/18.312181. 
[3] 
E. H. Brown, Generalizations of the Kervaire invariant, Annals Math., 95 (1972), 368383. doi: 10.2307/1970804. 
[4] 
P. Fan and M. Darnell, Sequence Design for Communications Applications, John Wiley, 1996. 
[5] 
R. Gold, Maximal recursive sequences with $3$valued recursive crosscorrelation functions, IEEE Trans. Inf. Theory, 14 (1968), 154156. doi: 10.1109/TIT.1968.1054106. 
[6] 
T. Helleseth and P. V. Kumar, Sequences with low correlation, in Handbook of Coding Theory (eds. V.S. Pless and W.C. Huffman), Elsevier, Amsterdman, 1998. 
[7] 
W. Jiang, L. Hu, X. Tang and X. Zeng, New optimal quadriphase sequences with larger linear span, IEEE Trans. Inf. Theory, 55 (2009), 458470. doi: 10.1109/TIT.2008.2008122. 
[8] 
A. Johansen, T. Helleseth and X. Tang, The correlation distribution of quaternary sequences of period $2(2^n1)$, IEEE Trans. Inf. Theory, 54 (2008), 31303139. doi: 10.1109/TIT.2008.924727. 
[9] 
T. Kasami, Weight Distribution Formula for Some Class of Cyclic Codes, Coordinated Sci. Lab., Univ. Illinois UrbanaChampaign, Tech. Rep. R285, 1966. 
[10] 
S. H. Kim and J. S. No, New families of binary sequences with low crosscorrelation property, IEEE Trans. Inf. Theory, 49 (2003), 30593065. doi: 10.1109/TIT.2003.818399. 
[11] 
P. V. Kumar, T. Helleseth, A. R. Calderbank and A. R. Hammons, Large families of quaternary sequences with low correlation, IEEE Trans. Inf. Theory, 42 (1996), 579592. doi: 10.1109/18.485726. 
[12] 
N. Li, X. Tang, X. Zeng and L. Hu, On the correlation distributions of optimal quaternary sequence family $\mathcal U$ and optimal binary sequence family $\mathcal V$, IEEE Trans. Inf. Theory, 57 (2011), 38153824. doi: 10.1109/TIT.2011.2132670. 
[13] 
K.U. Schmidt, $\mathbb Z_4$valued quadratic forms and quaternary sequence families, IEEE Trans. Inf. Theory, 55 (2009), 58035810. doi: 10.1109/TIT.2009.2032818. 
[14] 
V. Sidelnikov, On mutual correlation of sequences, Soviet Math. Dokl., 12 (1971), 197201. 
[15] 
X. Tang and T. Helleseth, Generic construction of quaternary sequences of period $2N$ with low correlation from quaternary sequences of odd period $N$, IEEE Trans. Inf. Theory, 57 (2011), 22952300. doi: 10.1109/TIT.2011.2110290. 
[16] 
X. Tang, T. Helleseth and P. Fan, A new optimal quaternary sequence family of length $2(2^n1)$ obtained from the orthogonal transformation of families $\mathcal B$ and $\mathcal C$, Des. Codes Crypt., 53 (2009), 137148. doi: 10.1007/s106230099294y. 
[17] 
X. Tang, T. Helleseth, L. Hu and W. Jiang, Two new families of optimal binary sequences obtained from quaternary sequences, IEEE Trans. Inf. Theory, 55 (2009), 433436. doi: 10.1109/TIT.2009.2013023. 
[18] 
X. Tang and P. Udaya, A note on the optimal quadriphase sequences families, IEEE Trans. Inf. Theory, 53 (2007), 433436. doi: 10.1109/TIT.2006.887502. 
[19] 
X. Tang, P. Udaya and P. Fan, Quadriphase sequences obtained from binary quadratic form sequences, in Sequences and Their Applications  SETA 2004, 2005, 243254. doi: 10.1007/11423461_17. 
[20] 
P. Udaya, Polyphase and Frequency Hopping Sequences Obtained from Finite Rings, Ph.D thesis, Dept. Elec. Eng., Indian Inst. Technol., Kanpur, 1992. 
[21] 
P. Udaya and M. U. Siddiqi, Optimal and suboptimal quadriphase sequences derived from maximal length sequences over $\mathbb Z_4$, Appl. Algebra Eng. Commun. Comput., 9 (1998), 161191. doi: 10.1007/s002000050101. 
[22] 
L. R. Welch, Lower bounds on the maximum crosscorrelation on the signals, IEEE Trans. Inf. Theory, 20 (1974), 397399. doi: 10.1109/TIT.1974.1055219. 
show all references
References:
[1] 
S. Boztas, R. Hammons and P. V. Kumar, $4$phase sequences with nearoptimum correlation properties, IEEE Trans. Inf. Theory, 14 (1992), 11011113. doi: 10.1109/18.135649. 
[2] 
S. Boztas and P. V. Kumar, Binary sequences with Goldlike correlation but larger linear span, IEEE Trans. Inf. Theory, 40 (1994), 532537. doi: 10.1109/18.312181. 
[3] 
E. H. Brown, Generalizations of the Kervaire invariant, Annals Math., 95 (1972), 368383. doi: 10.2307/1970804. 
[4] 
P. Fan and M. Darnell, Sequence Design for Communications Applications, John Wiley, 1996. 
[5] 
R. Gold, Maximal recursive sequences with $3$valued recursive crosscorrelation functions, IEEE Trans. Inf. Theory, 14 (1968), 154156. doi: 10.1109/TIT.1968.1054106. 
[6] 
T. Helleseth and P. V. Kumar, Sequences with low correlation, in Handbook of Coding Theory (eds. V.S. Pless and W.C. Huffman), Elsevier, Amsterdman, 1998. 
[7] 
W. Jiang, L. Hu, X. Tang and X. Zeng, New optimal quadriphase sequences with larger linear span, IEEE Trans. Inf. Theory, 55 (2009), 458470. doi: 10.1109/TIT.2008.2008122. 
[8] 
A. Johansen, T. Helleseth and X. Tang, The correlation distribution of quaternary sequences of period $2(2^n1)$, IEEE Trans. Inf. Theory, 54 (2008), 31303139. doi: 10.1109/TIT.2008.924727. 
[9] 
T. Kasami, Weight Distribution Formula for Some Class of Cyclic Codes, Coordinated Sci. Lab., Univ. Illinois UrbanaChampaign, Tech. Rep. R285, 1966. 
[10] 
S. H. Kim and J. S. No, New families of binary sequences with low crosscorrelation property, IEEE Trans. Inf. Theory, 49 (2003), 30593065. doi: 10.1109/TIT.2003.818399. 
[11] 
P. V. Kumar, T. Helleseth, A. R. Calderbank and A. R. Hammons, Large families of quaternary sequences with low correlation, IEEE Trans. Inf. Theory, 42 (1996), 579592. doi: 10.1109/18.485726. 
[12] 
N. Li, X. Tang, X. Zeng and L. Hu, On the correlation distributions of optimal quaternary sequence family $\mathcal U$ and optimal binary sequence family $\mathcal V$, IEEE Trans. Inf. Theory, 57 (2011), 38153824. doi: 10.1109/TIT.2011.2132670. 
[13] 
K.U. Schmidt, $\mathbb Z_4$valued quadratic forms and quaternary sequence families, IEEE Trans. Inf. Theory, 55 (2009), 58035810. doi: 10.1109/TIT.2009.2032818. 
[14] 
V. Sidelnikov, On mutual correlation of sequences, Soviet Math. Dokl., 12 (1971), 197201. 
[15] 
X. Tang and T. Helleseth, Generic construction of quaternary sequences of period $2N$ with low correlation from quaternary sequences of odd period $N$, IEEE Trans. Inf. Theory, 57 (2011), 22952300. doi: 10.1109/TIT.2011.2110290. 
[16] 
X. Tang, T. Helleseth and P. Fan, A new optimal quaternary sequence family of length $2(2^n1)$ obtained from the orthogonal transformation of families $\mathcal B$ and $\mathcal C$, Des. Codes Crypt., 53 (2009), 137148. doi: 10.1007/s106230099294y. 
[17] 
X. Tang, T. Helleseth, L. Hu and W. Jiang, Two new families of optimal binary sequences obtained from quaternary sequences, IEEE Trans. Inf. Theory, 55 (2009), 433436. doi: 10.1109/TIT.2009.2013023. 
[18] 
X. Tang and P. Udaya, A note on the optimal quadriphase sequences families, IEEE Trans. Inf. Theory, 53 (2007), 433436. doi: 10.1109/TIT.2006.887502. 
[19] 
X. Tang, P. Udaya and P. Fan, Quadriphase sequences obtained from binary quadratic form sequences, in Sequences and Their Applications  SETA 2004, 2005, 243254. doi: 10.1007/11423461_17. 
[20] 
P. Udaya, Polyphase and Frequency Hopping Sequences Obtained from Finite Rings, Ph.D thesis, Dept. Elec. Eng., Indian Inst. Technol., Kanpur, 1992. 
[21] 
P. Udaya and M. U. Siddiqi, Optimal and suboptimal quadriphase sequences derived from maximal length sequences over $\mathbb Z_4$, Appl. Algebra Eng. Commun. Comput., 9 (1998), 161191. doi: 10.1007/s002000050101. 
[22] 
L. R. Welch, Lower bounds on the maximum crosscorrelation on the signals, IEEE Trans. Inf. Theory, 20 (1974), 397399. doi: 10.1109/TIT.1974.1055219. 
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