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New almost perfect, odd perfect, and perfect sequences from difference balanced functions with d-form property
1. | Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China |
2. | Science and Technology on Communication Security Laboratory, Maibox 810, Chengdu, Sichuan 610041, China |
3. | Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, Sichuan 610031, China |
4. | Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada |
By using shift sequences defined by difference balanced functions with d-form property, and column sequences defined by a mutually orthogonal almost perfect sequences pair, new almost perfect, odd perfect, and perfect sequences are obtained via interleaving method. Furthermore, the proposed perfect QAM+ sequences positively answer to the problem of the existence of perfect QAM+ sequences proposed by Boztaş and Udaya.
References:
[1] |
M. Antweiler,
Cross-correlation of p-ary GMW sequences, IEEE Trans. Inf. Theory, 40 (1994), 1253-1261.
doi: 10.1109/18.335941. |
[2] |
S. Bozta¸s and P. Udaya, Nonbinary sequences with perfect and nearly perfect autocorrelation, in ISIT 2010,2010,1300-1304. |
[3] |
P. Z. Fan and M. Darnell, Sequence Design for Communications Applications, Research Studies Press, London, 1996.
![]() |
[4] |
S. W. Golomb and G. Gong, Signal Design for Good Correlation: for Wireless Communication, Cryptography and Radar, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9780511546907.![]() ![]() ![]() |
[5] |
G. Gong,
Theory and applications of q-ary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400-411.
doi: 10.1109/18.370141. |
[6] |
T. Helleseth and G. Gong,
New binary sequences with ideal-level autocorrelation function, IEEE Trans. Inf. Theory, 154 (2002), 2868-2872.
doi: 10.1109/TIT.2002.804052. |
[7] |
A. Klapper,
d-form sequence: Families of sequences with low correlaltion values and large linear spans, IEEE Trans. Inf. Theory, 51 (1995), 1469-1477.
doi: 10.1109/18.370143. |
[8] |
E. I. Krengel, Almost-perfect and odd-perfect ternary sequences, in SETA 2004,2005,197-207.
doi: 10.1007/11423461_13. |
[9] |
C. E. Lee, On a New Class of 5-ary Sequences Exhibiting Ideal Periodic Autocorrelation Properties with Applications to Spread Specturm Systems, Ph. D thesis, Mississipi State Univ. , 1986. |
[10] |
C. E. Lee,
Perfect q-ary sequences from multiplicative characters over GF (p), Electr. lett., 28 (1992), 833-834.
doi: 10.1049/el:19920527. |
[11] |
H. D. Lüke and H. D. Schotten,
Odd-perfect almost binary correlation sequences, IEEE Trans. Aerosp. Electron. Syst., 31 (1995), 495-498.
|
[12] |
W. H. Mow, Even-odd transormation with application to multi-user CW radars, in 1996 IEEE 4th Int. Symp. Spread Spectrum Techn. Appl. Proc. , Mainz, 1996,191-193. |
[13] |
J.-S. No,
New cyclic diffrence sets with Singer parameters constructed from d-homogeneous function, Des. Codes Cryptogr., 33 (2004), 199-213.
doi: 10.1023/B:DESI.0000036246.52472.81. |
[14] |
A. Pott,
Difference triangles and negaperiodic autocorrelation functions, Discrete Math., 308 (2008), 2854-2861.
doi: 10.1016/j.disc.2006.06.048. |
[15] |
X. H. Tang, A note on d-form function with difference balanced property, preprint. |
[16] |
Y. Yang, G. Gong and X. H. Tang, Odd perfect sequences and sets of spreading sequences with zero or low odd periodic correlation zone, in SETA 2012,2012, 1-12.
doi: 10.1007/978-3-642-30615-0_1. |
[17] |
X. Y. Zeng, L. Hu and Q. C. Liu, A novel method for constructing almost perfect polyphase sequences, in WCC 2005,2006,346-353.
doi: 10.1007/11779360_27. |
show all references
References:
[1] |
M. Antweiler,
Cross-correlation of p-ary GMW sequences, IEEE Trans. Inf. Theory, 40 (1994), 1253-1261.
doi: 10.1109/18.335941. |
[2] |
S. Bozta¸s and P. Udaya, Nonbinary sequences with perfect and nearly perfect autocorrelation, in ISIT 2010,2010,1300-1304. |
[3] |
P. Z. Fan and M. Darnell, Sequence Design for Communications Applications, Research Studies Press, London, 1996.
![]() |
[4] |
S. W. Golomb and G. Gong, Signal Design for Good Correlation: for Wireless Communication, Cryptography and Radar, Cambridge University Press, Cambridge, 2005.
doi: 10.1017/CBO9780511546907.![]() ![]() ![]() |
[5] |
G. Gong,
Theory and applications of q-ary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400-411.
doi: 10.1109/18.370141. |
[6] |
T. Helleseth and G. Gong,
New binary sequences with ideal-level autocorrelation function, IEEE Trans. Inf. Theory, 154 (2002), 2868-2872.
doi: 10.1109/TIT.2002.804052. |
[7] |
A. Klapper,
d-form sequence: Families of sequences with low correlaltion values and large linear spans, IEEE Trans. Inf. Theory, 51 (1995), 1469-1477.
doi: 10.1109/18.370143. |
[8] |
E. I. Krengel, Almost-perfect and odd-perfect ternary sequences, in SETA 2004,2005,197-207.
doi: 10.1007/11423461_13. |
[9] |
C. E. Lee, On a New Class of 5-ary Sequences Exhibiting Ideal Periodic Autocorrelation Properties with Applications to Spread Specturm Systems, Ph. D thesis, Mississipi State Univ. , 1986. |
[10] |
C. E. Lee,
Perfect q-ary sequences from multiplicative characters over GF (p), Electr. lett., 28 (1992), 833-834.
doi: 10.1049/el:19920527. |
[11] |
H. D. Lüke and H. D. Schotten,
Odd-perfect almost binary correlation sequences, IEEE Trans. Aerosp. Electron. Syst., 31 (1995), 495-498.
|
[12] |
W. H. Mow, Even-odd transormation with application to multi-user CW radars, in 1996 IEEE 4th Int. Symp. Spread Spectrum Techn. Appl. Proc. , Mainz, 1996,191-193. |
[13] |
J.-S. No,
New cyclic diffrence sets with Singer parameters constructed from d-homogeneous function, Des. Codes Cryptogr., 33 (2004), 199-213.
doi: 10.1023/B:DESI.0000036246.52472.81. |
[14] |
A. Pott,
Difference triangles and negaperiodic autocorrelation functions, Discrete Math., 308 (2008), 2854-2861.
doi: 10.1016/j.disc.2006.06.048. |
[15] |
X. H. Tang, A note on d-form function with difference balanced property, preprint. |
[16] |
Y. Yang, G. Gong and X. H. Tang, Odd perfect sequences and sets of spreading sequences with zero or low odd periodic correlation zone, in SETA 2012,2012, 1-12.
doi: 10.1007/978-3-642-30615-0_1. |
[17] |
X. Y. Zeng, L. Hu and Q. C. Liu, A novel method for constructing almost perfect polyphase sequences, in WCC 2005,2006,346-353.
doi: 10.1007/11779360_27. |
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