In 2007 Jedwab and Parker proposed [10] that the natural viewpoint for a Golay complementary sequence is as a projection of a multi-dimensional Golay array. In 2008 Fiedler, Jedwab and Parker [5] used this viewpoint to show how to construct and enumerate all known 2-phase Golay sequences of length 2, starting from two sources of Golay seed pairs. The first source of seed pairs is the trivial Go...

We argue that a Golay complementary sequence is naturally viewed as a projection of a multidimensional 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; an...

We introduce the notion of canonical form for Golay sequences such that every equivalence class contains exactly one member having the canonical form. Golay and Turyn have shown how to multiply Golay sequences of length m with Golay sequences of length n in order to construct Golay sequences of length mn. We say that Golay sequences of length n are constructible if they can be manufactured from...

Golay sequences have been used extensively for constructing base sequences, Yang numbers, T-sequences, Hadamard matrices, SBIBDs and Hadamard matrices with maximum possible sums. The possibility of obtaining new Golay sequences is diminishing and only non-existence results are appearing nowadays. We introduce block Golay sequences. It turns out that every result on Golay sequences could be exte...

Apart from the ordinary and the periodic Golay pairs, we define also the negaperiodic Golay pairs. (They occurred first, under a different name, in a paper of Ito.) If a Hadamard matrix is also a Toeplitz matrix, we show that it must be either cyclic or negacyclic. We investigate the construction of Hadamard (and weighing matrices) from two negacyclic blocks (2N-type). The Hadamard matrices of ...

In this paper, based on binary Golay complementary sequences, we propose some methods to construct Golay complementary sequences of length 2 for integer n, over the M-QAM constellation and 2M -Q-PAM constellations ,where M = 2 for integer m . A method to judge whether a sequence constructed using the new general offset pairs over the QAM constellation is Golay complementary sequence is proposed...

Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single H-ary Golay sequence and 4-QAM Golay complementary sequence with a large zero autocorrelation zone, where H ≥ 2 is an arbitrary even integer and q ≥ 2 is an arbitrary integer. Those new results on G...

In this paper,we present new constructions for M -QAM and 2M Q-PAM Golay complementary sequences of length 2 for integer n, where M = 2 for integer m. New decision conditions are proposed to judge whether the sequences with offset pairs proposed by Ying Li are Golay complementary, and with the new decision conditions, we prove the conjecture 1 and point out some drawbacks in conjecture 2 propos...

A general decoding method for cyclic codes is presented which gives promise of substantially reducing the complexity of decoders at the cost of a modest increase in decoding time (or delay). Significant reductions in decoder complexity for binary cyclic finite-geometry codes are demonstrated, and two decoding options for the Golay code are presented.

Constructions and nonexistence conditions for multi-dimensional Golay complementary array pairs are reviewed. A construction for a d-dimensional Golay array pair from a (d+1)-dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence results in the binary case.