-
Previous Article
On the number of bent functions from iterative constructions: lower bounds and hypotheses
- AMC Home
- This Issue
-
Next Article
Codes over $\mathbb{Z}_{2^k}$, Gray map and self-dual codes
The merit factor of binary arrays derived from the quadratic character
1. | Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada |
References:
[1] |
S. Alquaddoomi and R. A. Scholtz, On the nonexistence of Barker arrays and related matters, IEEE Trans. Inform. Theory, 35 (1989), 1048-1057.
doi: 10.1109/18.42220. |
[2] |
L. Bömer and M. Antweiler, Optimizing the aperiodic merit factor of binary arrays, Signal Process, 30 (1993), 1-13.
doi: 10.1016/0165-1684(93)90047-E. |
[3] |
L. Bömer, M. Antweiler and H. Schotten, Quadratic residue arrays, Frequenz, 47 (1993), 190-196.
doi: 10.1515/FREQ.1993.47.7-8.190. |
[4] |
P. Borwein, K.-K. S. Choi, and J. Jedwab, Binary sequences with merit factor greater than $6.34$, IEEE Trans. Inform. Theory, 50 (2004), 3234-3249.
doi: 10.1109/TIT.2004.838341. |
[5] |
D. Calabro and J. K. Wolf, On the synthesis of two-dimensional arrays with desirable correlation properties, Inform. Control, 11 (1967), 537-560.
doi: 10.1016/S0019-9958(67)90755-3. |
[6] |
J. A. Davis, J. Jedwab and K. W. Smith, Proof of the Barker array conjecture, Proc. Amer. Math. Soc., 135 (2007), 2011-2018.
doi: 10.1090/S0002-9939-07-08703-5. |
[7] |
H. Eggers, "Synthese zweidimensionaler Folgen mit guten Autokorrelationseigenschaften,'' Ph.D thesis, RWTH Aachen, Germany, 1986. |
[8] |
T. A. Gulliver and M. G. Parker, The multivariate merit factor of a Boolean function, in "Coding and Complexity'' (ed. M.J. Dinneen), IEEE, (2005), 58-62. |
[9] |
T. Høholdt and H. E. Jensen, Determination of the merit factor of Legendre sequences, IEEE Trans. Inform. Theory, 34 (1988), 161-164.
doi: 10.1109/18.2620. |
[10] |
T. Høholdt, H. E. Jensen and J. Justesen, Aperiodic correlations and the merit factor of a class of binary sequences, IEEE Trans. Inform. Theory, IT-31 (1985), 549-552.
doi: 10.1109/TIT.1985.1057071. |
[11] |
J. Jedwab, A survey of the merit factor problem for binary sequences, in "Sequences and Their Applications'' (eds. T. Helleseth et al.), Springer-Verlag, (2005), 30-55.
doi: 10.1007/11423461_2. |
[12] |
J. Jedwab and K.-U. Schmidt, The merit factor of binary sequence families constructed from $m$-sequences, Contemp. Math., 518 (2010), 265-278. |
[13] |
J. Jedwab and K.-U. Schmidt, The $L_4$ norm of Littlewood polynomials derived from the Jacobi symbol,, to appear in Pacific J. Math., ().
|
[14] |
H. E. Jensen and T. Høholdt, Binary sequences with good correlation properties, in "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes'' (eds. L. Huguet and A. Poli), Springer-Verlag, (1989), 306-320. |
[15] |
J. M. Jensen, H. E. Jensen and T. Høholdt, The merit factor of binary sequences related to difference sets, IEEE Trans. Inform. Theory, 37 (1991), 617-626.
doi: 10.1109/18.79917. |
[16] |
R. Lidl and H. Niederreiter, "Finite Fields,'' 2nd edition, Cambridge University Press, 1997. |
[17] |
J. E. Littlewood, "Some Problems in Real and Complex Analysis,'' D. C. Heath and Co. Raytheon Education Co., Lexington, MA, 1968. |
[18] |
M. J. Mossinghoff, Wieferich pairs and Barker sequences, Des. Codes Cryptogr., 53 (2009), 149-163.
doi: 10.1007/s10623-009-9301-3. |
[19] |
D. V. Sarwate, Mean-square correlation of shift-register sequences, IEE Proc., 131 (1984), 101-106. |
[20] |
K.-U. Schmidt, J. Jedwab and M. G. Parker, Two binary sequence families with large merit factor, Adv. Math. Commun., 3 (2009), 135-156.
doi: 10.3934/amc.2009.3.135. |
[21] |
M. R. Schroeder, "Number Theory in Science and Communication: with Applications in Cryptography, Physics, Digital Information, Computing, and Self-similarity,'' 3rd edition, Springer, Berlin, 1997. |
[22] |
R. Turyn and J. Storer, On binary sequences, Proc. Amer. Math. Soc., 12 (1961), 394-399.
doi: 10.1090/S0002-9939-1961-0125026-2. |
[23] |
R. G. van Schyndel, A. Z. Tirkel, I. D. Svalbe, T. E. Hall and C. F. Osborne, Algebraic construction of a new class of quasi-orthogonal arrays for steganography, Proc. SPIE, 3657 (1999), 354-364.
doi: 10.1117/12.344685. |
show all references
References:
[1] |
S. Alquaddoomi and R. A. Scholtz, On the nonexistence of Barker arrays and related matters, IEEE Trans. Inform. Theory, 35 (1989), 1048-1057.
doi: 10.1109/18.42220. |
[2] |
L. Bömer and M. Antweiler, Optimizing the aperiodic merit factor of binary arrays, Signal Process, 30 (1993), 1-13.
doi: 10.1016/0165-1684(93)90047-E. |
[3] |
L. Bömer, M. Antweiler and H. Schotten, Quadratic residue arrays, Frequenz, 47 (1993), 190-196.
doi: 10.1515/FREQ.1993.47.7-8.190. |
[4] |
P. Borwein, K.-K. S. Choi, and J. Jedwab, Binary sequences with merit factor greater than $6.34$, IEEE Trans. Inform. Theory, 50 (2004), 3234-3249.
doi: 10.1109/TIT.2004.838341. |
[5] |
D. Calabro and J. K. Wolf, On the synthesis of two-dimensional arrays with desirable correlation properties, Inform. Control, 11 (1967), 537-560.
doi: 10.1016/S0019-9958(67)90755-3. |
[6] |
J. A. Davis, J. Jedwab and K. W. Smith, Proof of the Barker array conjecture, Proc. Amer. Math. Soc., 135 (2007), 2011-2018.
doi: 10.1090/S0002-9939-07-08703-5. |
[7] |
H. Eggers, "Synthese zweidimensionaler Folgen mit guten Autokorrelationseigenschaften,'' Ph.D thesis, RWTH Aachen, Germany, 1986. |
[8] |
T. A. Gulliver and M. G. Parker, The multivariate merit factor of a Boolean function, in "Coding and Complexity'' (ed. M.J. Dinneen), IEEE, (2005), 58-62. |
[9] |
T. Høholdt and H. E. Jensen, Determination of the merit factor of Legendre sequences, IEEE Trans. Inform. Theory, 34 (1988), 161-164.
doi: 10.1109/18.2620. |
[10] |
T. Høholdt, H. E. Jensen and J. Justesen, Aperiodic correlations and the merit factor of a class of binary sequences, IEEE Trans. Inform. Theory, IT-31 (1985), 549-552.
doi: 10.1109/TIT.1985.1057071. |
[11] |
J. Jedwab, A survey of the merit factor problem for binary sequences, in "Sequences and Their Applications'' (eds. T. Helleseth et al.), Springer-Verlag, (2005), 30-55.
doi: 10.1007/11423461_2. |
[12] |
J. Jedwab and K.-U. Schmidt, The merit factor of binary sequence families constructed from $m$-sequences, Contemp. Math., 518 (2010), 265-278. |
[13] |
J. Jedwab and K.-U. Schmidt, The $L_4$ norm of Littlewood polynomials derived from the Jacobi symbol,, to appear in Pacific J. Math., ().
|
[14] |
H. E. Jensen and T. Høholdt, Binary sequences with good correlation properties, in "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes'' (eds. L. Huguet and A. Poli), Springer-Verlag, (1989), 306-320. |
[15] |
J. M. Jensen, H. E. Jensen and T. Høholdt, The merit factor of binary sequences related to difference sets, IEEE Trans. Inform. Theory, 37 (1991), 617-626.
doi: 10.1109/18.79917. |
[16] |
R. Lidl and H. Niederreiter, "Finite Fields,'' 2nd edition, Cambridge University Press, 1997. |
[17] |
J. E. Littlewood, "Some Problems in Real and Complex Analysis,'' D. C. Heath and Co. Raytheon Education Co., Lexington, MA, 1968. |
[18] |
M. J. Mossinghoff, Wieferich pairs and Barker sequences, Des. Codes Cryptogr., 53 (2009), 149-163.
doi: 10.1007/s10623-009-9301-3. |
[19] |
D. V. Sarwate, Mean-square correlation of shift-register sequences, IEE Proc., 131 (1984), 101-106. |
[20] |
K.-U. Schmidt, J. Jedwab and M. G. Parker, Two binary sequence families with large merit factor, Adv. Math. Commun., 3 (2009), 135-156.
doi: 10.3934/amc.2009.3.135. |
[21] |
M. R. Schroeder, "Number Theory in Science and Communication: with Applications in Cryptography, Physics, Digital Information, Computing, and Self-similarity,'' 3rd edition, Springer, Berlin, 1997. |
[22] |
R. Turyn and J. Storer, On binary sequences, Proc. Amer. Math. Soc., 12 (1961), 394-399.
doi: 10.1090/S0002-9939-1961-0125026-2. |
[23] |
R. G. van Schyndel, A. Z. Tirkel, I. D. Svalbe, T. E. Hall and C. F. Osborne, Algebraic construction of a new class of quasi-orthogonal arrays for steganography, Proc. SPIE, 3657 (1999), 354-364.
doi: 10.1117/12.344685. |
[1] |
Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135 |
[2] |
Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237-244. doi: 10.3934/amc.2017015 |
[3] |
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) : 475-484. doi: 10.3934/amc.2013.7.475 |
[4] |
Ji-Woong Jang, Young-Sik Kim, Sang-Hyo Kim. New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set. Advances in Mathematics of Communications, 2009, 3 (2) : 115-124. doi: 10.3934/amc.2009.3.115 |
[5] |
Xiaohui Liu, Jinhua Wang, Dianhua Wu. Two new classes of binary sequence pairs with three-level cross-correlation. Advances in Mathematics of Communications, 2015, 9 (1) : 117-128. doi: 10.3934/amc.2015.9.117 |
[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] |
Arne Winterhof, Zibi Xiao. Binary sequences derived from differences of consecutive quadratic residues. Advances in Mathematics of Communications, 2022, 16 (1) : 83-93. doi: 10.3934/amc.2020100 |
[8] |
Moulay Rchid Sidi Ammi, Ismail Jamiai. Finite difference and Legendre spectral method for a time-fractional diffusion-convection equation for image restoration. Discrete and Continuous Dynamical Systems - S, 2018, 11 (1) : 103-117. doi: 10.3934/dcdss.2018007 |
[9] |
Amer Rasheed, Aziz Belmiloudi, Fabrice Mahé. Dynamics of dendrite growth in a binary alloy with magnetic field effect. Conference Publications, 2011, 2011 (Special) : 1224-1233. doi: 10.3934/proc.2011.2011.1224 |
[10] |
Chun-Hao Teng, I-Liang Chern, Ming-Chih Lai. Simulating binary fluid-surfactant dynamics by a phase field model. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1289-1307. doi: 10.3934/dcdsb.2012.17.1289 |
[11] |
Hélène Hibon, Ying Hu, Shanjian Tang. Mean-field type quadratic BSDEs. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022009 |
[12] |
Guangmei Shao, Wei Xue, Gaohang Yu, Xiao Zheng. Improved SVRG for finite sum structure optimization with application to binary classification. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2253-2266. doi: 10.3934/jimo.2019052 |
[13] |
Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zero-sum linear-quadratic differential game: Saddle-point equilibrium sequence. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 1-20. doi: 10.3934/naco.2017001 |
[14] |
Yoshikazu Katayama, Colin E. Sutherland and Masamichi Takesaki. The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions. Electronic Research Announcements, 1995, 1: 43-47. |
[15] |
Grégory Berhuy, Jean Fasel, Odile Garotta. Rank weights for arbitrary finite field extensions. Advances in Mathematics of Communications, 2021, 15 (4) : 575-587. doi: 10.3934/amc.2020083 |
[16] |
Martino Bardi. Explicit solutions of some linear-quadratic mean field games. Networks and Heterogeneous Media, 2012, 7 (2) : 243-261. doi: 10.3934/nhm.2012.7.243 |
[17] |
Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic mean-field-game of backward stochastic differential systems. Mathematical Control and Related Fields, 2018, 8 (3&4) : 653-678. doi: 10.3934/mcrf.2018028 |
[18] |
Olivier Guéant. New numerical methods for mean field games with quadratic costs. Networks and Heterogeneous Media, 2012, 7 (2) : 315-336. doi: 10.3934/nhm.2012.7.315 |
[19] |
Zhenghong Qiu, Jianhui Huang, Tinghan Xie. Linear-Quadratic-Gaussian mean-field controls of social optima. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021047 |
[20] |
Denis Danilov, Britta Nestler. Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1035-1047. doi: 10.3934/dcds.2006.15.1035 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]