This fact was observed for the cases of PRBS and complementary codes , particularly with the Golay code pairs.
Applications of Extended Optimal Filters to Golay Code Pairs
The performance analysis for Barker, PRBS and Golay codes is presented in Subsections 3.1, 3.2 and 3.3, respectively.
One could say that each particle in the triality diagram brings in its 8-bit Hamming code word to temporarily form the 24-bit binary Golay code word or, equivalently, the 12-bit ternary Golay code word, related to the Leech lattice.
On Construction of the (24, 12, 8) Golay Codes. arXiv: cs/0607074v1.