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The crosscorrelation distribution of a $p$ary $m$sequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$
1.  College of Sciences, China University of Petroleum, 66 Changjiang Xilu, Qingdao, Shandong 266580, China, China 
2.  State Key Laboratory of Integrated Service Networks, Xidian University, 2 Taibai Nanlu, Xi'an, Shannxi 710071, China, China 
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$,, Finite Fields Appl., 10 (2004), 285. doi: 10.1016/j.ffa.2003.08.004. Google Scholar 
[2] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary $m$sequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^{2}}{2(p+1)}$,, IEEE Trans. Inf. Theory, 58 (2012), 1873. doi: 10.1109/TIT.2011.2177573. Google Scholar 
[3] 
H. Dobbertin, T. Helleseth, P. V. Kumar and H. Martinsen, Ternary $m$sequences with threevalued crosscorrelation function: new decimations of Welch and Niho type,, IEEE Trans. Inf. Theory, 47 (2001), 1473. doi: 10.1109/18.923728. Google Scholar 
[4] 
T. Helleseth, Some results about the crosscorrelation function between two maximal linear sequences,, Discrete Math., 16 (1976), 209. doi: 10.1016/0012365X(76)90100X. Google Scholar 
[5] 
T. Helleseth and P. V. Kumar, Sequences with low correlation,, in Handbook of Coding Theory (eds. V. Pless and C. Huffman), (1998), 1765. Google Scholar 
[6] 
R. Lidl and H. Niederreiter, Finite Fields,, AddisonWesley, (1983). Google Scholar 
[7] 
J. Luo and K. Feng, On the weight distributions of two classes of cyclic codes,, IEEE Trans. Inf. Theory, 54 (2008), 5332. doi: 10.1109/TIT.2008.2006424. Google Scholar 
[8] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued crosscorrelation,, in Proceedings of IWSDA'11, (2011), 44. doi: 10.1109/IWSDA.2011.6159435. Google Scholar 
[9] 
E. N. Müller, On the crosscorrelation of sequences over $GF(p)$ with short periods,, IEEE Trans. Inf. Theory, 45 (1999), 289. Google Scholar 
[10] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of $p$ary $m$sequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$,, IEEE Trans. Inf. Theory, 54 (2008), 3140. doi: 10.1109/TIT.2008.924694. Google Scholar 
[11] 
T. Storer, Cyclotomy and Difference Sets,, Markham, (1967). Google Scholar 
show all references
References:
[1] 
A. W. Bluher, On $x^{q+1}+ax+b$,, Finite Fields Appl., 10 (2004), 285. doi: 10.1016/j.ffa.2003.08.004. Google Scholar 
[2] 
S. T. Choi, J. S. No and H. Chung, On the crosscorrelation of a $p$ary $m$sequence of period $p^{2m}1$ and its decimated sequence by $\frac{(p^m+1)^{2}}{2(p+1)}$,, IEEE Trans. Inf. Theory, 58 (2012), 1873. doi: 10.1109/TIT.2011.2177573. Google Scholar 
[3] 
H. Dobbertin, T. Helleseth, P. V. Kumar and H. Martinsen, Ternary $m$sequences with threevalued crosscorrelation function: new decimations of Welch and Niho type,, IEEE Trans. Inf. Theory, 47 (2001), 1473. doi: 10.1109/18.923728. Google Scholar 
[4] 
T. Helleseth, Some results about the crosscorrelation function between two maximal linear sequences,, Discrete Math., 16 (1976), 209. doi: 10.1016/0012365X(76)90100X. Google Scholar 
[5] 
T. Helleseth and P. V. Kumar, Sequences with low correlation,, in Handbook of Coding Theory (eds. V. Pless and C. Huffman), (1998), 1765. Google Scholar 
[6] 
R. Lidl and H. Niederreiter, Finite Fields,, AddisonWesley, (1983). Google Scholar 
[7] 
J. Luo and K. Feng, On the weight distributions of two classes of cyclic codes,, IEEE Trans. Inf. Theory, 54 (2008), 5332. doi: 10.1109/TIT.2008.2006424. Google Scholar 
[8] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued crosscorrelation,, in Proceedings of IWSDA'11, (2011), 44. doi: 10.1109/IWSDA.2011.6159435. Google Scholar 
[9] 
E. N. Müller, On the crosscorrelation of sequences over $GF(p)$ with short periods,, IEEE Trans. Inf. Theory, 45 (1999), 289. Google Scholar 
[10] 
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Crosscorrelation distribution of $p$ary $m$sequence of period $p^{4k}1$ and its decimated sequences by $(\frac{p^{2k}+1}{2})^{2}$,, IEEE Trans. Inf. Theory, 54 (2008), 3140. doi: 10.1109/TIT.2008.924694. Google Scholar 
[11] 
T. Storer, Cyclotomy and Difference Sets,, Markham, (1967). Google Scholar 
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