Determination of the merit factor of Legendre sequences
IEEE Transactions on Information Theory
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
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
EURASIP Journal on Applied 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
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
New construction for binary sequences of period pm-1 with optimal autocorrelation using (z+1)d+azd+b
IEEE Transactions on Information Theory
Almost difference sets and their sequences with optimal autocorrelation
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
New Binary Sequences With Optimal Autocorrelation Magnitude
IEEE Transactions on Information Theory
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
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
Advances in the merit factor problem for binary sequences
Journal of Combinatorial Theory Series A
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The perfect binary sequence of period 4 - '0111' (or cyclic shifts of itself or its complement) - has the optimal periodic autocorrelation function where all out-of-phase values are zero. Not surprisingly, it is also the Barker sequence of length 4 where all out-of-phase aperiodic autocorrelation values have the magnitudes of at most one. From these observations, the applications of the sequence for low periodic and aperiodic autocorrelations are studied. First, the perfect sequence is discussed for binary sequences with optimal periodic autocorrelation. New binary sequences of period N = 4(2m - 1), m = 2k with optimal periodic autocorrelation are presented, which are obtained by a slight modification of product sequences of binary m-sequences and the perfect sequence. Then, it is observed that a product sequence of the Legendre and the perfect sequences has not only the optimal periodic but also the good aperiodic autocorrelations with the asymptotic merit factor 6. Moreover, if the product sequences replace Legendre sequences in Borwein, Choi, Jedwab (BCJ) sequences, or equivalently Kristiansen-Parker sequences (simply BCJ-KP sequences), numerical results show that the resulting sequences have the same asymptotic merit factor as the BCJ-KP sequences.