Determination of the merit factor of Legendre sequences
IEEE Transactions on Information Theory
The L4 norm of a polynomial with coefficients
American Mathematical Monthly
Optimizing the aperiodic merit factor of binary arrays
Signal Processing
A survey of partial difference sets
Designs, Codes and Cryptography
A survey of Hadamard difference sets
GDSTM '93 Proceedings of a special research quarter on Groups, difference sets, and the monster
Rudin-Shapiro-like polynomials in L4
Mathematics of Computation
A New Family of Ternary Sequences with IdealTwo-level Autocorrelation Function
Designs, Codes and Cryptography
Shift Register Sequences
SIAM Review
Binary Sequences with Good Correlation Properties
AAECC-5 Proceedings of the 5th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Designs, Codes and Cryptography
Evolutionary search for low autocorrelated binary sequences
IEEE Transactions on Evolutionary Computation
Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes
IEEE Transactions on Information Theory
Binary sequences with merit factor greater than 6.34
IEEE Transactions on Information Theory
Binary sequences with merit factor 6.3
IEEE Transactions on Information Theory
There are no Barker arrays having more than two dimensions
Designs, Codes and Cryptography
Golay complementary array pairs
Designs, Codes and Cryptography
The Peak to Sidelobe Level of the Most Significant Bit of Trace Codes over Galois Rings
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
New algorithms for designing unimodular sequences with good correlation properties
IEEE Transactions on Signal Processing
The perfect binary sequence of period 4 for low periodic and aperiodic autocorrelations
SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Binary sequences with good aperiodic autocorrelations using cross-entropy method
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
Appended m-sequences with merit factor greater than 3.34
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Univariate and multivariate merit factors
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
The density of ternary barker sequences
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Advances in the merit factor problem for binary sequences
Journal of Combinatorial Theory Series A
| Hi-index | 0.00 |
A classical problem of digital sequence design, first studied in the 1950s but still not well understood, is to determine those binary sequences whose aperiodic autocorrelations are collectively small according to some suitable measure. The merit factor is an important such measure, and the problem of determining the best value of the merit factor of long binary sequences has resisted decades of attack by mathematicians and communications engineers. In equivalent guise, the determination of the best asymptotic merit factor is an unsolved problem in complex analysis proposed by Littlewood in the 1960s that until recently was studied along largely independent lines. The same problem is also studied in theoretical physics and theoretical chemistry as a notoriously difficult combinatorial optimisation problem. The best known value for the asymptotic merit factor has remained unchanged since 1988. However recent experimental and theoretical results strongly suggest a possible improvement. This survey describes the development of our understanding of the merit factor problem by bringing together results from several disciplines, and places the recent results within their historical and scientific framework.