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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, N-5020 Bergen |
References:
[1] |
S. Boztas, R. Hammons and P. V. Kumar, $4$-phase sequences with near-optimum correlation properties, IEEE Trans. Inf. Theory, 14 (1992), 1101-1113.
doi: 10.1109/18.135649. |
[2] |
S. Boztas and P. V. Kumar, Binary sequences with Gold-like correlation but larger linear span, IEEE Trans. Inf. Theory, 40 (1994), 532-537.
doi: 10.1109/18.312181. |
[3] |
E. H. Brown, Generalizations of the Kervaire invariant, Annals Math., 95 (1972), 368-383.
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), 154-156.
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), 458-470.
doi: 10.1109/TIT.2008.2008122. |
[8] |
A. Johansen, T. Helleseth and X. Tang, The correlation distribution of quaternary sequences of period $2(2^n-1)$, IEEE Trans. Inf. Theory, 54 (2008), 3130-3139.
doi: 10.1109/TIT.2008.924727. |
[9] |
T. Kasami, Weight Distribution Formula for Some Class of Cyclic Codes, Coordinated Sci. Lab., Univ. Illinois Urbana-Champaign, Tech. Rep. R-285, 1966. |
[10] |
S. H. Kim and J. S. No, New families of binary sequences with low crosscorrelation property, IEEE Trans. Inf. Theory, 49 (2003), 3059-3065.
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), 579-592.
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), 3815-3824.
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), 5803-5810.
doi: 10.1109/TIT.2009.2032818. |
[14] |
V. Sidelnikov, On mutual correlation of sequences, Soviet Math. Dokl., 12 (1971), 197-201. |
[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), 2295-2300.
doi: 10.1109/TIT.2011.2110290. |
[16] |
X. Tang, T. Helleseth and P. Fan, A new optimal quaternary sequence family of length $2(2^n-1)$ obtained from the orthogonal transformation of families $\mathcal B$ and $\mathcal C$, Des. Codes Crypt., 53 (2009), 137-148.
doi: 10.1007/s10623-009-9294-y. |
[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), 433-436.
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), 433-436.
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, 243-254.
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), 161-191.
doi: 10.1007/s002000050101. |
[22] |
L. R. Welch, Lower bounds on the maximum crosscorrelation on the signals, IEEE Trans. Inf. Theory, 20 (1974), 397-399.
doi: 10.1109/TIT.1974.1055219. |
show all references
References:
[1] |
S. Boztas, R. Hammons and P. V. Kumar, $4$-phase sequences with near-optimum correlation properties, IEEE Trans. Inf. Theory, 14 (1992), 1101-1113.
doi: 10.1109/18.135649. |
[2] |
S. Boztas and P. V. Kumar, Binary sequences with Gold-like correlation but larger linear span, IEEE Trans. Inf. Theory, 40 (1994), 532-537.
doi: 10.1109/18.312181. |
[3] |
E. H. Brown, Generalizations of the Kervaire invariant, Annals Math., 95 (1972), 368-383.
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), 154-156.
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), 458-470.
doi: 10.1109/TIT.2008.2008122. |
[8] |
A. Johansen, T. Helleseth and X. Tang, The correlation distribution of quaternary sequences of period $2(2^n-1)$, IEEE Trans. Inf. Theory, 54 (2008), 3130-3139.
doi: 10.1109/TIT.2008.924727. |
[9] |
T. Kasami, Weight Distribution Formula for Some Class of Cyclic Codes, Coordinated Sci. Lab., Univ. Illinois Urbana-Champaign, Tech. Rep. R-285, 1966. |
[10] |
S. H. Kim and J. S. No, New families of binary sequences with low crosscorrelation property, IEEE Trans. Inf. Theory, 49 (2003), 3059-3065.
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), 579-592.
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), 3815-3824.
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), 5803-5810.
doi: 10.1109/TIT.2009.2032818. |
[14] |
V. Sidelnikov, On mutual correlation of sequences, Soviet Math. Dokl., 12 (1971), 197-201. |
[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), 2295-2300.
doi: 10.1109/TIT.2011.2110290. |
[16] |
X. Tang, T. Helleseth and P. Fan, A new optimal quaternary sequence family of length $2(2^n-1)$ obtained from the orthogonal transformation of families $\mathcal B$ and $\mathcal C$, Des. Codes Crypt., 53 (2009), 137-148.
doi: 10.1007/s10623-009-9294-y. |
[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), 433-436.
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), 433-436.
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, 243-254.
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), 161-191.
doi: 10.1007/s002000050101. |
[22] |
L. R. Welch, Lower bounds on the maximum crosscorrelation on the signals, IEEE Trans. Inf. Theory, 20 (1974), 397-399.
doi: 10.1109/TIT.1974.1055219. |
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