A theory of ternary complementary pairs
Journal of Combinatorial Theory Series A
Golay complementary array pairs
Designs, Codes and Cryptography
Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes
IEEE Transactions on Information Theory
Generalized Reed-Muller codes and power control in OFDM modulation
IEEE Transactions on Information Theory
A new construction of 16-QAM Golay complementary sequences
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On cosets of the generalized first-order reed-muller code with low PMEPR
IEEE Transactions on Information Theory
How Do More Golay Sequences Arise?
IEEE Transactions on Information Theory
A Framework for the Construction ofGolay Sequences
IEEE Transactions on Information Theory
Close Encounters with Boolean Functions of Three Different Kinds
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
New QAM golay complementary pairs with unequal sequence power
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Note: A new source of seed pairs for Golay sequences of length 2m
Journal of Combinatorial Theory Series A
New 64-QAM Golay complementary sequences
IEEE Transactions on Information Theory
A construction of general QAM Golay complementary sequences
IEEE Transactions on Information Theory
Quaternary Golay sequence pairs I: even length
Designs, Codes and Cryptography
On logic functions of complementary arrays of length 2n
AIC'10/BEBI'10 Proceedings of the 10th WSEAS international conference on applied informatics and communications, and 3rd WSEAS international conference on Biomedical electronics and biomedical informatics
Generalised complementary arrays
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Wavelength isolation sequence pairs
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
A complementary construction using mutually unbiased bases
Cryptography and Communications
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We argue that a Golay complementary sequence is naturally viewed as a projection of a multi-dimensional Golay array. We present a three-stage process for constructing and enumerating Golay array and sequence pairs:1.construct suitable Golay array pairs from lower-dimensional Golay array pairs; 2.apply transformations to these Golay array pairs to generate a larger set of Golay array pairs; and 3.take projections of the resulting Golay array pairs to lower dimensions. This process greatly simplifies previous approaches, by separating the construction of Golay arrays from the enumeration of all possible projections of these arrays to lower dimensions. We use this process to construct and enumerate all 2^h-phase Golay sequences of length 2^m obtainable under any known method, including all 4-phase Golay sequences obtainable from the length 16 examples given in 2005 by Li and Chu [Y. Li, W.B. Chu, More Golay sequences, IEEE Trans. Inform. Theory 51 (2005) 1141-1145].