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Some designs and codes invariant under the Tits group
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 
References:
[1] 
M. Antweiler, Crosscorrelation of pary GMW sequences, IEEE Trans. Inf. Theory, 40 (1994), 12531261. 
[2] 
S. Bozta¸s and P. Udaya, Nonbinary sequences with perfect and nearly perfect autocorrelation, in ISIT 2010,2010,13001304. 
[3]  P. Z. Fan, M. Darnell, Sequence Design for Communications Applications, Research Studies Press, London, 1996. 
[4]  S. W. Golomb, G. Gong, Signal Design for Good Correlation: for Wireless Communication, Cryptography and Radar, Cambridge University Press, Cambridge, 2005. 
[5] 
G. Gong, Theory and applications of qary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400411. 
[6] 
T. Helleseth, G. Gong, New binary sequences with ideallevel autocorrelation function, IEEE Trans. Inf. Theory, 154 (2002), 28682872. 
[7] 
A. Klapper, dform sequence: Families of sequences with low correlaltion values and large linear spans, IEEE Trans. Inf. Theory, 51 (1995), 14691477. 
[8] 
E. I. Krengel, Almostperfect and oddperfect ternary sequences, in SETA 2004,2005,197207. 
[9] 
C. E. Lee, On a New Class of 5ary Sequences Exhibiting Ideal Periodic Autocorrelation Properties with Applications to Spread Specturm Systems, Ph. D thesis, Mississipi State Univ. , 1986. 
[10] 
C. E. Lee, Perfect qary sequences from multiplicative characters over GF (p), Electr. lett., 28 (1992), 833834. 
[11] 
H. D. Lüke, H. D. Schotten, Oddperfect almost binary correlation sequences, IEEE Trans. Aerosp. Electron. Syst., 31 (1995), 495498. 
[12] 
W. H. Mow, Evenodd transormation with application to multiuser CW radars, in 1996 IEEE 4th Int. Symp. Spread Spectrum Techn. Appl. Proc. , Mainz, 1996,191193. 
[13] 
J.S. No, New cyclic diffrence sets with Singer parameters constructed from dhomogeneous function, Des. Codes Cryptogr., 33 (2004), 199213. 
[14] 
A. Pott, Difference triangles and negaperiodic autocorrelation functions, Discrete Math., 308 (2008), 28542861. 
[15] 
X. H. Tang, A note on dform 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, 112. 
[17] 
X. Y. Zeng, L. Hu and Q. C. Liu, A novel method for constructing almost perfect polyphase sequences, in WCC 2005,2006,346353. 
show all references
References:
[1] 
M. Antweiler, Crosscorrelation of pary GMW sequences, IEEE Trans. Inf. Theory, 40 (1994), 12531261. 
[2] 
S. Bozta¸s and P. Udaya, Nonbinary sequences with perfect and nearly perfect autocorrelation, in ISIT 2010,2010,13001304. 
[3]  P. Z. Fan, M. Darnell, Sequence Design for Communications Applications, Research Studies Press, London, 1996. 
[4]  S. W. Golomb, G. Gong, Signal Design for Good Correlation: for Wireless Communication, Cryptography and Radar, Cambridge University Press, Cambridge, 2005. 
[5] 
G. Gong, Theory and applications of qary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400411. 
[6] 
T. Helleseth, G. Gong, New binary sequences with ideallevel autocorrelation function, IEEE Trans. Inf. Theory, 154 (2002), 28682872. 
[7] 
A. Klapper, dform sequence: Families of sequences with low correlaltion values and large linear spans, IEEE Trans. Inf. Theory, 51 (1995), 14691477. 
[8] 
E. I. Krengel, Almostperfect and oddperfect ternary sequences, in SETA 2004,2005,197207. 
[9] 
C. E. Lee, On a New Class of 5ary Sequences Exhibiting Ideal Periodic Autocorrelation Properties with Applications to Spread Specturm Systems, Ph. D thesis, Mississipi State Univ. , 1986. 
[10] 
C. E. Lee, Perfect qary sequences from multiplicative characters over GF (p), Electr. lett., 28 (1992), 833834. 
[11] 
H. D. Lüke, H. D. Schotten, Oddperfect almost binary correlation sequences, IEEE Trans. Aerosp. Electron. Syst., 31 (1995), 495498. 
[12] 
W. H. Mow, Evenodd transormation with application to multiuser CW radars, in 1996 IEEE 4th Int. Symp. Spread Spectrum Techn. Appl. Proc. , Mainz, 1996,191193. 
[13] 
J.S. No, New cyclic diffrence sets with Singer parameters constructed from dhomogeneous function, Des. Codes Cryptogr., 33 (2004), 199213. 
[14] 
A. Pott, Difference triangles and negaperiodic autocorrelation functions, Discrete Math., 308 (2008), 28542861. 
[15] 
X. H. Tang, A note on dform 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, 112. 
[17] 
X. Y. Zeng, L. Hu and Q. C. Liu, A novel method for constructing almost perfect polyphase sequences, in WCC 2005,2006,346353. 
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