Citation: |
[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. |