Abstract
The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker involving multi-dimensional Golay arrays, and a “sum–difference” construction that modifies a result due to Eliahou, Kervaire and Saffari. The existence of 4-phase seed pairs of lengths 3, 5, 11, and 13 is assumed; their origin is considered in (Gibson and Jedwab, Des Codes Cryptogr, 2010).
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Gibson, R.G., Jedwab, J. Quaternary Golay sequence pairs I: even length. Des. Codes Cryptogr. 59, 131–146 (2011). https://doi.org/10.1007/s10623-010-9471-z
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DOI: https://doi.org/10.1007/s10623-010-9471-z