This thesis classifies all ordered quaternary Golay sequence pairs of length less than 22. Previous results, both classical and recent, are applied to explain the existence pattern for all even lengths less than 22. In addition, a general construction is developed which derives quaternary Golay pairs of length congruent to 5 modulo 8 from binary Barker sequences of the same odd length. Applying this construction to lengths 5 and 13 explains all such known pairs. Furthermore, this thesis explores the possibility of reversing the Barker-to-Golay derivation by attempting to construct an odd-length binary Barker sequence from a quaternary Golay sequence of the same length. This procedure is successful for all quaternary Golay sequences of length congruent to 5 modulo 8 satisfying certain conditions. Since there are no binary Barker sequences of odd length greater than 13, all quaternary Golay sequences fulfilling these conditions are known.
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