
Previous Article
On the dual of (non)weakly regular bent functions and selfdual bent functions
 AMC Home
 This Issue

Next Article
Small Golay sequences
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. 
[1] 
Wenbing Chen, Jinquan Luo, Yuansheng Tang, Quanquan Liu. Some new results on cross correlation of $p$ary $m$sequence and its decimated sequence. Advances in Mathematics of Communications, 2015, 9 (3) : 375390. doi: 10.3934/amc.2015.9.375 
[2] 
Hua Liang, Jinquan Luo, Yuansheng Tang. On crosscorrelation of a binary $m$sequence of period $2^{2k}1$ and its decimated sequences by $(2^{lk}+1)/(2^l+1)$. Advances in Mathematics of Communications, 2017, 11 (4) : 693703. doi: 10.3934/amc.2017050 
[3] 
Xiaohui Liu, Jinhua Wang, Dianhua Wu. Two new classes of binary sequence pairs with threelevel crosscorrelation. Advances in Mathematics of Communications, 2015, 9 (1) : 117128. doi: 10.3934/amc.2015.9.117 
[4] 
Yanfeng Qi, Chunming Tang, Zhengchun Zhou, Cuiling Fan. Several infinite families of pary weakly regular bent functions. Advances in Mathematics of Communications, 2018, 12 (2) : 303315. doi: 10.3934/amc.2018019 
[5] 
Lanqiang Li, Shixin Zhu, Li Liu. The weight distribution of a class of pary cyclic codes and their applications. Advances in Mathematics of Communications, 2019, 13 (1) : 137156. doi: 10.3934/amc.2019008 
[6] 
Huaning Liu, Xi Liu. On the correlation measures of orders $ 3 $ and $ 4 $ of binary sequence of period $ p^2 $ derived from Fermat quotients. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021008 
[7] 
Zilong Wang, Guang Gong. Correlation of binary sequence families derived from the multiplicative characters of finite fields. Advances in Mathematics of Communications, 2013, 7 (4) : 475484. doi: 10.3934/amc.2013.7.475 
[8] 
Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequencyhopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 5562. doi: 10.3934/amc.2015.9.55 
[9] 
Hua Liang, Wenbing Chen, Jinquan Luo, Yuansheng Tang. A new nonbinary sequence family with low correlation and large size. Advances in Mathematics of Communications, 2017, 11 (4) : 671691. doi: 10.3934/amc.2017049 
[10] 
Ferruh Özbudak, Eda Tekin. Correlation distribution of a sequence family generalizing some sequences of Trachtenberg. Advances in Mathematics of Communications, 2021, 15 (4) : 647662. doi: 10.3934/amc.2020087 
[11] 
Zhenyu Zhang, Lijia Ge, Fanxin Zeng, Guixin Xuan. Zero correlation zone sequence set with intergroup orthogonal and intersubgroup complementary properties. Advances in Mathematics of Communications, 2015, 9 (1) : 921. doi: 10.3934/amc.2015.9.9 
[12] 
Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal lowhitzone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 6779. doi: 10.3934/amc.2018004 
[13] 
Qing Liu, Bingo WingKuen Ling, Qingyun Dai, Qing Miao, Caixia Liu. Optimal maximally decimated Mchannel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming. Journal of Industrial and Management Optimization, 2021, 17 (4) : 19932011. doi: 10.3934/jimo.2020055 
[14] 
Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237244. doi: 10.3934/amc.2017015 
[15] 
Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zerosum linearquadratic differential game: Saddlepoint equilibrium sequence. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 120. doi: 10.3934/naco.2017001 
[16] 
Yixiao Qiao, Xiaoyao Zhou. Zero sequence entropy and entropy dimension. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 435448. doi: 10.3934/dcds.2017018 
[17] 
Walter Briec, Bernardin Solonandrasana. Some remarks on a successive projection sequence. Journal of Industrial and Management Optimization, 2006, 2 (4) : 451466. doi: 10.3934/jimo.2006.2.451 
[18] 
KaiUwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135156. doi: 10.3934/amc.2009.3.135 
[19] 
Matthew Macauley, Henning S. Mortveit. Update sequence stability in graph dynamical systems. Discrete and Continuous Dynamical Systems  S, 2011, 4 (6) : 15331541. doi: 10.3934/dcdss.2011.4.1533 
[20] 
Wenjun Xia, Jinzhi Lei. Formulation of the protein synthesis rate with sequence information. Mathematical Biosciences & Engineering, 2018, 15 (2) : 507522. doi: 10.3934/mbe.2018023 
2021 Impact Factor: 1.015
Tools
Metrics
Other articles
by authors
[Back to Top]