All 4096 vectors in the code are at . . .

**http://neilsloane.com/oadir/oa.4096.12.2.7.txt.**

Sloane’s list* contains the 12 generating vectors

listed in 2011 by Adlam —

As noted by Conway in *Sphere Packings, Lattices and Groups* ,

these 4096 vectors, constructed lexicographically, are exactly

the same vectors produced by using the Conway-Sloane version

of the Curtis Miracle Octad Generator (MOG). Conway says this

lexico-MOG equivalence was first discovered by M. J. T. Guy.

(Of course, *any* permutation of the 24 columns above produces

a version of the code *qua* code. But because the lexicographic and

the MOG constructions yield the same result, that result is in

some sense canonical.)

See my post of July 13, 2020 —

**The lexicographic Golay code
contains, embedded within it,
the Miracle Octad Generator.**

For some related results, Google the twelfth generator:

* Sloane’s list is of the codewords as the rows of an *orthogonal array* —

See also http://neilsloane.com/oadir/.