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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), 273307. 
[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), 5669. 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), 18151823. 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, 17651853. 
[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), 37683774. 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), 12201224. 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, 311315. 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), 579592. doi: 10.1109/18.485726. 
[10] 
V. M. Sidel'nikov, Some $k$valued pseudorandom sequences and nearly equidistant codes, Probl. Inf. Transm., 5 (1969), 1216. 
[11] 
V. M. Sidel'nikov, On mutual correlation of sequences, Soviet Math. Dokl, 12 (1971), 197201. 
[12] 
D. Wan, Generators and irreducible polynomials over finite fields, Math. Comput., 66 (1997), 11951212. doi: 10.1090/S0025571897008351. 
[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), 39903998. doi: 10.1109/TIT.2013.2243496. 
[14] 
A. Weil, On some exponential sums, Proc. Natl. Acad. Sci. USA, 34 (1948), 204207. 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), 397399. 
[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), 63766387. 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), 40614070. doi: 10.1109/TIT.2010.2050793. 
show all references
References:
[1] 
P. Deligne, La conjecture de Weil I, Publ. Math. IHES, 43 (1974), 273307. 
[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), 5669. 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), 18151823. 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, 17651853. 
[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), 37683774. 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), 12201224. 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, 311315. 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), 579592. doi: 10.1109/18.485726. 
[10] 
V. M. Sidel'nikov, Some $k$valued pseudorandom sequences and nearly equidistant codes, Probl. Inf. Transm., 5 (1969), 1216. 
[11] 
V. M. Sidel'nikov, On mutual correlation of sequences, Soviet Math. Dokl, 12 (1971), 197201. 
[12] 
D. Wan, Generators and irreducible polynomials over finite fields, Math. Comput., 66 (1997), 11951212. doi: 10.1090/S0025571897008351. 
[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), 39903998. doi: 10.1109/TIT.2013.2243496. 
[14] 
A. Weil, On some exponential sums, Proc. Natl. Acad. Sci. USA, 34 (1948), 204207. 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), 397399. 
[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), 63766387. 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), 40614070. doi: 10.1109/TIT.2010.2050793. 
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