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($\sigma,\delta$)-codes
Correlation of binary sequence families derived from the multiplicative characters of finite fields
1. | State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, Shanxi 710071, China |
2. | Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada |
References:
[1] |
P. Deligne, La conjecture de Weil I, Publ. Math. IHES, 43 (1974), 273-307. |
[2] |
S. W. Golomb and G. Gong, Signal Design with Good Correlation: for Wireless Communications, Cryptography and Radar Applications, Cambridge University Press, 2005.
doi: 10.1017/CBO9780511546907. |
[3] |
L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56-69.
doi: 10.1016/j.jnt.2003.12.002. |
[4] |
Y. K. Han and K. Yang, New $M$-ary sequence families with low correlation and large size, IEEE Trans. Inf. Theory, 55 (2009), 1815-1823.
doi: 10.1109/TIT.2009.2013040. |
[5] |
T. Helleseth and P. V. Kumar, Sequences with low correlation, in Handbook of Coding Theory (eds. V. Pless and C. Huffman), Elsevier Science Publishers, 1998, 1765-1853. |
[6] |
Y. Kim, J. Chung, J. S. No and H. Chung, New families of $M$-ary sequences with low correlation constructed from Sidel'nikov sequences, IEEE Trans. Inf. Theory, 54 (2008), 3768-3774.
doi: 10.1109/TIT.2008.926428. |
[7] |
Y. J. Kim and H. Y. Song, Cross correlation of Sidel'nikov sequences and their constant multiples, IEEE Trans. Inf. Theory, 53 (2007), 1220-1224.
doi: 10.1109/TIT.2006.890723. |
[8] |
Y. J. Kim, H. Y. Song, G. Gong and H. Chung, Crosscorrelation of $q$-ary power residue sequences of period $p$, in Proc. IEEE ISIT, 2006, 311-315.
doi: 10.1109/ISIT.2006.261604. |
[9] |
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. |
[10] |
V. M. Sidel'nikov, Some $k$-valued pseudo-random sequences and nearly equidistant codes, Probl. Inf. Transm., 5 (1969), 12-16. |
[11] |
V. M. Sidel'nikov, On mutual correlation of sequences, Soviet Math. Dokl, 12 (1971), 197-201. |
[12] |
D. Wan, Generators and irreducible polynomials over finite fields, Math. Comput., 66 (1997), 1195-1212.
doi: 10.1090/S0025-5718-97-00835-1. |
[13] |
Z. Wang and G. Gong, New polyphase sequence families with low correlation derived from the Weil bound of exponential sums, IEEE Trans. Inf. Theory, 59 (2013), 3990-3998.
doi: 10.1109/TIT.2013.2243496. |
[14] |
A. Weil, On some exponential sums, Proc. Natl. Acad. Sci. USA, 34 (1948), 204-207.
doi: 10.1073/pnas.34.5.204. |
[15] |
L. R. Welch, Lower bounds on the minimum correlation of signal, IEEE Trans. Inf. Theory, 20 (1974), 397-399. |
[16] |
N. Y. Yu and G. Gong, Multiplicative characters, the Weil Bound, and polyphase sequence families with low correlation, IEEE Trans. Inf. Theory, 56 (2010), 6376-6387.
doi: 10.1109/TIT.2010.2079590. |
[17] |
N. Y. Yu and G. Gong, New construction of $M$-ary sequence families with low correlation from the structure of Sidelnikov sequences, IEEE Trans. Inf. Theory, 56 (2010), 4061-4070.
doi: 10.1109/TIT.2010.2050793. |
show all references
References:
[1] |
P. Deligne, La conjecture de Weil I, Publ. Math. IHES, 43 (1974), 273-307. |
[2] |
S. W. Golomb and G. Gong, Signal Design with Good Correlation: for Wireless Communications, Cryptography and Radar Applications, Cambridge University Press, 2005.
doi: 10.1017/CBO9780511546907. |
[3] |
L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56-69.
doi: 10.1016/j.jnt.2003.12.002. |
[4] |
Y. K. Han and K. Yang, New $M$-ary sequence families with low correlation and large size, IEEE Trans. Inf. Theory, 55 (2009), 1815-1823.
doi: 10.1109/TIT.2009.2013040. |
[5] |
T. Helleseth and P. V. Kumar, Sequences with low correlation, in Handbook of Coding Theory (eds. V. Pless and C. Huffman), Elsevier Science Publishers, 1998, 1765-1853. |
[6] |
Y. Kim, J. Chung, J. S. No and H. Chung, New families of $M$-ary sequences with low correlation constructed from Sidel'nikov sequences, IEEE Trans. Inf. Theory, 54 (2008), 3768-3774.
doi: 10.1109/TIT.2008.926428. |
[7] |
Y. J. Kim and H. Y. Song, Cross correlation of Sidel'nikov sequences and their constant multiples, IEEE Trans. Inf. Theory, 53 (2007), 1220-1224.
doi: 10.1109/TIT.2006.890723. |
[8] |
Y. J. Kim, H. Y. Song, G. Gong and H. Chung, Crosscorrelation of $q$-ary power residue sequences of period $p$, in Proc. IEEE ISIT, 2006, 311-315.
doi: 10.1109/ISIT.2006.261604. |
[9] |
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. |
[10] |
V. M. Sidel'nikov, Some $k$-valued pseudo-random sequences and nearly equidistant codes, Probl. Inf. Transm., 5 (1969), 12-16. |
[11] |
V. M. Sidel'nikov, On mutual correlation of sequences, Soviet Math. Dokl, 12 (1971), 197-201. |
[12] |
D. Wan, Generators and irreducible polynomials over finite fields, Math. Comput., 66 (1997), 1195-1212.
doi: 10.1090/S0025-5718-97-00835-1. |
[13] |
Z. Wang and G. Gong, New polyphase sequence families with low correlation derived from the Weil bound of exponential sums, IEEE Trans. Inf. Theory, 59 (2013), 3990-3998.
doi: 10.1109/TIT.2013.2243496. |
[14] |
A. Weil, On some exponential sums, Proc. Natl. Acad. Sci. USA, 34 (1948), 204-207.
doi: 10.1073/pnas.34.5.204. |
[15] |
L. R. Welch, Lower bounds on the minimum correlation of signal, IEEE Trans. Inf. Theory, 20 (1974), 397-399. |
[16] |
N. Y. Yu and G. Gong, Multiplicative characters, the Weil Bound, and polyphase sequence families with low correlation, IEEE Trans. Inf. Theory, 56 (2010), 6376-6387.
doi: 10.1109/TIT.2010.2079590. |
[17] |
N. Y. Yu and G. Gong, New construction of $M$-ary sequence families with low correlation from the structure of Sidelnikov sequences, IEEE Trans. Inf. Theory, 56 (2010), 4061-4070.
doi: 10.1109/TIT.2010.2050793. |
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