Leech Lattice from Z4 Golay Code via Gray Map Yields 196560 Vectors — E8 Intelligence Research

July 24, 2026Open Access

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Key Points

To investigate the construction of the Leech lattice from the Z4 Golay code using the Gray map and its implications for group theory.
Constructed the Leech lattice using Z4 Golay code with minimum Lee weight 12 and applied Gray map for transformation.
Calculated the kissing number and minimum norm of the lattice, linking it to the Monster group and E8 root system.
Constructed 196560 minimal vectors from the Leech lattice.
Confirmed the kissing number of the Leech lattice as 196560, correlating with E8 root system calculations.
Established a mathematical link between the Leech lattice and the Monster group's significance in number theory.

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Shows the construction of a leech lattice in 24 dimensions, revealing connections to the Monster group and E8 system.

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Andrew Stewart Caldin (2026) studied this question.

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