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An improved certificateless strong keyinsulated signature scheme in the standard model
Some new results on cross correlation of $p$ary $m$sequence and its decimated sequence
1.  School of Mathemetics & Computation Science, Anqing Normal University, Anqing, Anhui 246133, China 
2.  Department of Mathematic and Statistics, Centtal China Normal University, Wuhan, Hubei 430079, China 
3.  Department of Mathematic Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, China, China 
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$, Finite Fields Appl., 10 (2004), 285305. doi: 10.1016/j.ffa.2003.08.004. Google Scholar 
[2] 
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications, in Proc. ISIT'14, 2014, 31453149. Google Scholar 
[3] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a ternary msequence of period $3^{4k+2}1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8, in Proc. ISIT'10, 2010, 12681271. Google Scholar 
[4] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary msequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$, IEEE Trans. Inf. Theory, 58 (2012), 18731879. doi: 10.1109/TIT.2011.2177573. Google Scholar 
[5] 
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums, IEEE Trans. Inf. Theory, 52 (2006), 613627. doi: 10.1109/TIT.2005.862094. Google Scholar 
[6] 
T. Helleseth, Some results about the crosscorrelation function between two maximallinear sequence, Discrete Math., 16 (1976), 209232. Google Scholar 
[7] 
R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Boston, 1983. Google Scholar 
[8] 
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 53325344. doi: 10.1109/TIT.2008.2006424. Google Scholar 
[9] 
J. Luo and K. Feng, Cyclic codes and sequences from generalized CoulterMatthews function, IEEE Trans. Inf. Theory, 54 (2008), 53455353. doi: 10.1109/TIT.2008.2006394. Google Scholar 
[10] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued cross correlation, in Proc. IWSDA'11, 2011, 4447. Google Scholar 
[11] 
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, (). Google Scholar 
[12] 
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the CoulterMatthews decimation, IEEE Trans. Inf. Theory, 52 (2006), 22412247. doi: 10.1109/TIT.2006.872857. Google Scholar 
[13] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of pary msequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$, IEEE Trans. Inf. Theory, 54 (2008),31403149. doi: 10.1109/TIT.2008.924694. Google Scholar 
[14] 
Y. Sun, Z. Wang, H. Li and T. Yan, The crosscorrelation distribution of a $p$ary msequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$, Adv. Math. Commun., 7 (2013), 409424. doi: 10.3934/amc.2013.7.409. Google Scholar 
[15] 
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on crosscorrelation distribution between a $p$ary $m$sequence and its decimated sequences, IEEE Trans. Inf. Theory, 60 (2014), 73687381. doi: 10.1109/TIT.2014.2350775. Google Scholar 
show all references
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$, Finite Fields Appl., 10 (2004), 285305. doi: 10.1016/j.ffa.2003.08.004. Google Scholar 
[2] 
W. Chen, J. Luo and Y. Tang, Exponential sums from half quadratic forms and its applications, in Proc. ISIT'14, 2014, 31453149. Google Scholar 
[3] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a ternary msequence of period $3^{4k+2}1$ and its decimated sequence by $(3^{2k+1}+1)^{2}$ over 8, in Proc. ISIT'10, 2010, 12681271. Google Scholar 
[4] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary msequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^2}{2(p+1)}$, IEEE Trans. Inf. Theory, 58 (2012), 18731879. doi: 10.1109/TIT.2011.2177573. Google Scholar 
[5] 
H. Dobbertin, P. Felke and T. Helleseth, Niho type cross correlation functions via Dickson polynomials and Kloosterman sums, IEEE Trans. Inf. Theory, 52 (2006), 613627. doi: 10.1109/TIT.2005.862094. Google Scholar 
[6] 
T. Helleseth, Some results about the crosscorrelation function between two maximallinear sequence, Discrete Math., 16 (1976), 209232. Google Scholar 
[7] 
R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Boston, 1983. Google Scholar 
[8] 
J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 53325344. doi: 10.1109/TIT.2008.2006424. Google Scholar 
[9] 
J. Luo and K. Feng, Cyclic codes and sequences from generalized CoulterMatthews function, IEEE Trans. Inf. Theory, 54 (2008), 53455353. doi: 10.1109/TIT.2008.2006394. Google Scholar 
[10] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued cross correlation, in Proc. IWSDA'11, 2011, 4447. Google Scholar 
[11] 
J, Luo, Y. Tang and H. Wang, Exponential sums, cyclic codes and sequences: the odd characteristic Kasami case,, preprint, (). Google Scholar 
[12] 
G. J. Ness, T. Helleseth and A. Kholosha, On the correlation distribution of the CoulterMatthews decimation, IEEE Trans. Inf. Theory, 52 (2006), 22412247. doi: 10.1109/TIT.2006.872857. Google Scholar 
[13] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of pary msequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$, IEEE Trans. Inf. Theory, 54 (2008),31403149. doi: 10.1109/TIT.2008.924694. Google Scholar 
[14] 
Y. Sun, Z. Wang, H. Li and T. Yan, The crosscorrelation distribution of a $p$ary msequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^k+1)^2}{2(p^e+1)}$, Adv. Math. Commun., 7 (2013), 409424. doi: 10.3934/amc.2013.7.409. Google Scholar 
[15] 
Y. Xia, C. Li, X. Zeng and T. Helleseth, Some results on crosscorrelation distribution between a $p$ary $m$sequence and its decimated sequences, IEEE Trans. Inf. Theory, 60 (2014), 73687381. doi: 10.1109/TIT.2014.2350775. Google Scholar 
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