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Small Golay sequences
The cross-correlation 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), 285-305.
doi: 10.1016/j.ffa.2003.08.004. |
[2] |
S. T. Choi, J. S. No and H. Chung, On the cross-correlation 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), 1873-1879.
doi: 10.1109/TIT.2011.2177573. |
[3] |
H. Dobbertin, T. Helleseth, P. V. Kumar and H. Martinsen, Ternary $m$-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type, IEEE Trans. Inf. Theory, 47 (2001), 1473-1481.
doi: 10.1109/18.923728. |
[4] |
T. Helleseth, Some results about the cross-correlation function between two maximal linear sequences, Discrete Math., 16 (1976), 209-232.
doi: 10.1016/0012-365X(76)90100-X. |
[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, 1765-1853. |
[6] |
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Boston, 1983. |
[7] |
J. Luo and K. Feng, On the weight distributions of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 5332-5344.
doi: 10.1109/TIT.2008.2006424. |
[8] |
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with six-valued cross-correlation, in Proceedings of IWSDA'11, (2011), 44-47.
doi: 10.1109/IWSDA.2011.6159435. |
[9] |
E. N. Müller, On the cross-correlation of sequences over $GF(p)$ with short periods, IEEE Trans. Inf. Theory, 45 (1999), 289-295. |
[10] |
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Cross-correlation 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), 3140-3149.
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), 285-305.
doi: 10.1016/j.ffa.2003.08.004. |
[2] |
S. T. Choi, J. S. No and H. Chung, On the cross-correlation 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), 1873-1879.
doi: 10.1109/TIT.2011.2177573. |
[3] |
H. Dobbertin, T. Helleseth, P. V. Kumar and H. Martinsen, Ternary $m$-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type, IEEE Trans. Inf. Theory, 47 (2001), 1473-1481.
doi: 10.1109/18.923728. |
[4] |
T. Helleseth, Some results about the cross-correlation function between two maximal linear sequences, Discrete Math., 16 (1976), 209-232.
doi: 10.1016/0012-365X(76)90100-X. |
[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, 1765-1853. |
[6] |
R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Boston, 1983. |
[7] |
J. Luo and K. Feng, On the weight distributions of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 5332-5344.
doi: 10.1109/TIT.2008.2006424. |
[8] |
J. Luo, T. Helleseth and A. Kholosha, Two nonbinary sequences with six-valued cross-correlation, in Proceedings of IWSDA'11, (2011), 44-47.
doi: 10.1109/IWSDA.2011.6159435. |
[9] |
E. N. Müller, On the cross-correlation of sequences over $GF(p)$ with short periods, IEEE Trans. Inf. Theory, 45 (1999), 289-295. |
[10] |
E. Y. Seo, Y. S. Kim, J. S. No and D. J. Shin, Cross-correlation 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), 3140-3149.
doi: 10.1109/TIT.2008.924694. |
[11] |
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. |
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