A new source of seed pairs for Golay sequences of length 2m

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 2h -phase Golay sequences of length 2m , starting from two sources of Golay seed pairs. The first source of seed pairs is the trivial Golay pair of length 1, which gives rise to “standard” Golay sequences; the second source is the set of 512 non-standard “cross-over” 4-phase Golay pairs of length 8, which give rise to non-standard 4-phase Golay sequences of length 2m for each m ≥ 4. Beginning with a single length 5 complex-valued Golay sequence pair, we show how to construct a third source of Golay seed pairs (and only the second known non-trivial source), namely a new set of 5184 non-standard 6-phase Golay sequences of length 16 that form 62208 non-standard ordered Golay pairs. Using the multi-dimensional viewpoi...

• Type: Journal
• Year: 2010
• Where: JCT
• Authors: Frank Fiedler, Jonathan Jedwab, Amy Wiebe
• Keywords: Golay Pairs, Golay Sequence, JCT 2010, Non-standard Golay Sequences