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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), 285305. doi: 10.1016/j.ffa.2003.08.004. 
[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), 18731879. doi: 10.1109/TIT.2011.2177573. 
[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), 14731481. doi: 10.1109/18.923728. 
[4] 
T. Helleseth, Some results about the crosscorrelation function between two maximal linear sequences, Discrete Math., 16 (1976), 209232. doi: 10.1016/0012365X(76)90100X. 
[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] 
R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Boston, 1983. 
[7] 
J. Luo and K. Feng, On the weight distributions of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 53325344. doi: 10.1109/TIT.2008.2006424. 
[8] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued crosscorrelation, in Proceedings of IWSDA'11, (2011), 4447. doi: 10.1109/IWSDA.2011.6159435. 
[9] 
E. N. Müller, On the crosscorrelation of sequences over $GF(p)$ with short periods, IEEE Trans. Inf. Theory, 45 (1999), 289295. 
[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), 31403149. doi: 10.1109/TIT.2008.924694. 
[11] 
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. 
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. 
[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), 18731879. doi: 10.1109/TIT.2011.2177573. 
[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), 14731481. doi: 10.1109/18.923728. 
[4] 
T. Helleseth, Some results about the crosscorrelation function between two maximal linear sequences, Discrete Math., 16 (1976), 209232. doi: 10.1016/0012365X(76)90100X. 
[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] 
R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Boston, 1983. 
[7] 
J. Luo and K. Feng, On the weight distributions of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 53325344. doi: 10.1109/TIT.2008.2006424. 
[8] 
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with sixvalued crosscorrelation, in Proceedings of IWSDA'11, (2011), 4447. doi: 10.1109/IWSDA.2011.6159435. 
[9] 
E. N. Müller, On the crosscorrelation of sequences over $GF(p)$ with short periods, IEEE Trans. Inf. Theory, 45 (1999), 289295. 
[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), 31403149. doi: 10.1109/TIT.2008.924694. 
[11] 
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. 
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