Determination of the merit factor of Legendre sequences
IEEE Transactions on Information Theory
Finite fields
Rudin-Shapiro-like polynomials in L4
Mathematics of Computation
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
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
Appended m-sequences with merit factor greater than 3.34
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity
The merit factor problem for binary sequences
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A survey of the merit factor problem for binary sequences
SETA'04 Proceedings of the Third 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
A class of finite binary sequences with alternate auto-correlation values equal to zero (Corresp.)
IEEE Transactions on Information Theory
Sieves for low autocorrelation binary sequences
IEEE Transactions on Information Theory
The merit factor of long low autocorrelation binary sequences (Corresp.)
IEEE Transactions on Information Theory
The merit factor of Legendre sequences (Corresp.)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Aperiodic correlations and the merit factor of a class of binary sequences (Corresp.)
IEEE Transactions on Information Theory
The merit factor of binary sequences related to difference sets
IEEE Transactions on Information Theory
Binary and quadriphase sequences with optimal autocorrelation properties: a survey
IEEE Transactions on Information Theory
Binary sequences with merit factor greater than 6.34
IEEE Transactions on Information Theory
Modifications of Modified Jacobi Sequences
IEEE Transactions on Information Theory
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The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications engineering and condensed matter physics. We establish the asymptotic merit factor of several families of binary sequences and thereby prove various conjectures, explain numerical evidence presented by other authors, and bring together within a single framework results previously appearing in scattered form. We exhibit, for the first time, families of skew-symmetric sequences whose asymptotic merit factor is as large as the best known value (an algebraic number greater than 6.34) for all binary sequences; this is interesting in light of Golay@?s conjecture that the subclass of skew-symmetric sequences has asymptotically optimal merit factor. Our methods combine Fourier analysis, estimation of character sums, and estimation of the number of lattice points in polyhedra.