Complex Golay sequences: Structure and applications (Q1613488)

In 1992, \textit{J. Seberry} and \textit{M. Yamada} [Contemporary design theory, Collect. Surv., 431-560 (1992; Zbl 0776.05028)] introduced the notion of complex Golay sequences, in order to generalize some constructions of Hadamard matrices. In the present paper, the authors present some new infinite classes of such sequences , establishing some facts about their structure. They show also that, if the length of complex Golay sequences is divisible by a prime \(p\) congruent with 3 mod 4, then their Hall polynomials have a nontrivial factorization which is given over GF\((p^2)\). This fact is used to simplify the search for complex Golay sequences and to construct a large variety of sets of four complex sequences with zero autrocorrelation, suitable for the construction of various matrices such as Hadamard matrices, complex Hadamard matrices and signed group Hadamard matrices over the dihedral signed group.