A New Class of <i>p</i>-Ary Sequence Families with Low Correlation Property via <i>m</i>-Sequence

REN Wenli; FU Fangwei

doi:10.1049/cje.2016.06.041

Volume 25 Issue 4

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REN Wenli and FU Fangwei, “A New Class of p-Ary Sequence Families with Low Correlation Property via m-Sequence,” Chinese Journal of Electronics, vol. 25, no. 4, pp. 678-685, 2016, doi: 10.1049/cje.2016.06.041

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REN Wenli and FU Fangwei, “A New Class of p-Ary Sequence Families with Low Correlation Property via m-Sequence,” Chinese Journal of Electronics, vol. 25, no. 4, pp. 678-685, 2016, doi: 10.1049/cje.2016.06.041

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A New Class of p-Ary Sequence Families with Low Correlation Property via m-Sequence

doi: 10.1049/cje.2016.06.041

REN Wenli¹,
FU Fangwei²

1.
College of Mathematical Sciences, Dezhou University, Dezhou 253023, China;
2.
Chern Institute of Mathematics, Nankai University, Tianjin 300071, China

Funds: This work is supported in part by the National Key Basic Research Program of China (No.2013CB834204), the National Natural Science Foundation of China (No.61171082), and A Project of Shandong Province Higher Educational Science and Technology Program (No.J14LI56).

Received Date: 2014-05-14
Rev Recd Date: 2014-08-16
Publish Date: 2016-07-10

Abstract

Abstract

For an odd prime p which is congruent to 3 module 4 and an odd integerk, we investigate the upper bound on the magnitude of cross correlation values of a p-Ary m-sequence s(t) and its decimated sequences s(dt+l) for a decimation value d. Using the above upper bound of the magnitude of cross correlation values of p-Ary m-Sequence and its decimated sequences, we construct a new class of p-Ary sequence families with low correlation property via m-Sequence.
- Cross correlation,
- Decimated sequence,
- m-Sequence,
- Quadratic form

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References(22)

References

S.T. Choi, T. Lim, J.S. No and H. Chung, "On the cross-correlation of a p-ary m-sequences of period p^2m-1 and its decimated sequences by (p^m+1)²/2(p+1)", IEEE Transactions on Information Theory, Vol.58, No.3, pp.1873-1879, 2012.

S.T. Choi, J.Y. Kim and J.S. No, "On the cross-correlation of p-ary m-sequences and its decimated sequences by d=pⁿ+1/p^k+1+pⁿ-1/2", IEICE Transactions on Communications, Vol.E96.B, No.9, pp.2190-2197, 2013.

H. Dobberbin, T. Helleseth, P.V. Kummar and H. Martinsen, "Ternaray m-sequences with three-valued cross-correlation function:New decimation of Welch and Niho type", IEEE Transactions on Information Theory, Vol.47, No.4, pp.1473-1481, 2001.

T. Helleseth, "Some results about the cross-correlation function between two maximal linear sequences", Discrete Mathematics, Vol.16, No.3, pp.209-232, 1976.

Z. Hu, X. Li, D. Mills, et al., "On the cross-correlation of sequences with the decimation factor d=pⁿ+1/p+1-pⁿ-1/2", Applicable Algebra in Engineering, Communication and Computing, Vol.12, No.3, pp.255-263, 2001.

E.N. Muller, "On the cross-correlstion of sequences over GF(p) with short periods", IEEE Transactions on Information Theory, Vol.45, No.1, pp.289-295, 1999.

G.J. Ness, T. Helleseth and A. Kholosha, "On the correlation distribution of the coulter-matthews decimation", IEEE Transactions on Information Theory, Vol.52, No.5, pp.2241-2247, 2006.

E.Y. Seo, Y.S. Kim, J.S. No and D.J. Shin, "Cross-correlation distribution of p-ary m-sequences of period p^4k-1 and its decimated sequences by p^2k+1/2)²", IEEE Transactions on Information Theory, Vol.54, No.7, pp.3140-3149, 2008.

H.M. Trachtenberg, "On the cross-correlation functions of maximal recurring sequences", Ph.D. thesis, University of Southern California, Los Angeles, USA, 1970.

Y. Xia, X. Zeng and L. Hu, "Further cross-correlation properties of sequences with the decimation factor d=pⁿ+1/p+1-pⁿ-1/2", Applicable Algebra in Engineering, Communication and Computing, Vol.21, No.5, pp.329-342, 2010.

S.T. Choi and J.S. No, "On the cross-correlation of p-ary m-sequences and their decimated sequences", IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences, Vol.E95-A, No.11, pp.1808-1818, 2012.

P.V. Kumar and O. Moreno, "Prime-phase sequencs with periodic correlation properties better than binary sequences", IEEE Transactions on Information Theory, Vol.37, No.3, pp.603-616, 1991.

J.W. Jang, Y.S. Kim, J.S. No and T. Helleseth, "New family of p-ary sequence with optimal correlation property and large linear span", IEEE Transactions on Information Theory, Vol.45, No.1, pp.289-295, 1999.

E.Y. Seo, Y.S. Kim, J.S. No and D.J. Shin, "Cross-correlation distribution of p-ary m-sequences and its p+1 decimated sequences with shorter period", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E90-A, No.11, pp.2568-2574, 2007.

X. Zeng, N. Li and L. Hu, "A class of nonbinary codes and sequence families", Sequences and Their Applications-SETA 2008, Lecture Notes in Computer Science, Vol.5023, No.10, pp.81-94, 2008.

J.Y. Kim, S.T. Choi, T. Lim, J.S. No and H. Chung, "On the cross-correlation of ternaray m-sequences of period 3^4k+2-1 with decimation 3^4k+2-3^2k+1+2/4+3^2k+1", The Proceedings of IEEE International Symposium on Information Theory, Cambridge, USA, pp.1014-1018, 2012.

Y. Xia, S. Chen, T. Hellesth and C. Li, "Cross-correlation between a p-ary m-sequence and its all decimated sequences for d=(p^m+1)(p^m+p-1)/p+1", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E97-A, No.4, pp.964-967, 2014.

R. Lidl and H. Niederreliter, "Finite Fields", Encyclopedia of Mathematics and its Applications, Addison-Wesley Publishing Company, The Netherlands, Vol.20, 1983.

A.W. Bluher, "On x^q+1+ax+b", Finite Fileds and Their Applications, Vol.10, No.3, pp.285-305, 2004.

R. Gold, "Maximal recursive sequences with 3-valued recursive cross-correlation function", IEEE Transactions on Information Theory, Vol.14, No.1, pp.154-156, 1968.

J.S. No and P.V. Kumar, "A new family of binary pseudorandom sequences having optimal periodic correlation properties and large linear span", IEEE Transactions on Information Theory, Vol.35, No.2, pp.371-379, 1989.

J.D. Olsen, R.A. Scholtz and L.R. Welch, "Bent-function sequences", IEEE Transactions on Information Theory, Vol.28, No.6, pp.858-864, 1982.

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