A multi-dimensional approach to the construction and enumeration of Golay complementary sequences
Journal of Combinatorial Theory Series A
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
Near-complementary sequences of various lengths and low PMEPR for multicarrier communications
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
New 64-QAM Golay complementary sequences
IEEE Transactions on Information Theory
A construction of general QAM Golay complementary sequences
IEEE Transactions on Information Theory
A new construction of 16-QAM near complementary sequences
IEEE Transactions on Information Theory
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
A complementary construction using mutually unbiased bases
Cryptography and Communications
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In 1999, Davis and Jedwab gave an explicit algebraic normal form for m!/2 - 2h(m+1) ordered Golay pairs of length 2mmiddot over Z2h, involving m!/2 - 2h(m+1) Golay sequences. In 2005, Li and Chu unexpectedly found an additional 1024 length 16 quaternary Golay sequences. Fiedler and Jedwab showed in 2006 that these new Golay sequences exist because of a "crossover" of the aperiodic autocorrelation function of certain quaternary length eight sequences belonging to Golay pairs, and that they spawn further new quaternary Golay sequences and pairs of length 2m for m > 4 under Budisin's 1990 iterative construction. The total number of Golay sequences and pairs spawned in this way is counted, and their algebraic normal form is given explicitly. A framework of constructions is derived in which Turyn's 1974 product construction, together with several variations, plays a key role. All previously known Golay sequences and pairs of length 2m over Z2h can be obtained directly in explicit algebraic normal form from this framework. Furthermore, additional quaternary Golay sequences and pairs of length 2m are produced that cannot be obtained from any other known construction. The framework generalizes readily to lengths that are not a power of 2, and to alphabets other than Z2h .