The above is about a subspace of the
24-dimensional vector space over GF(2)
. . . "An entire world of just 24 squares,"
to adapt a phrase from other Log24
posts tagged "Promises."
Update of 1:45 AM ET Sept. 18, 2022 —
It seems* from a Magma calculation that
the resemblance of the above extended
cube-motif code to the Golay code is only
superficial.
Without the highly symmetric generating codewords that were added
to extend its dimension from 8 to 12, the cube-motifs code apparently
does , like the Golay code, have nonzero weights of only 8, 12, 16, and 24 —
Perhaps someone can prove there is no way that adding more generating
codewords can turn the cube-motif code into the Golay code.
* The "seems" is because I have not yet encountered any of these
relatively rare (42 out of 4096) purported weight-4 codewords. Their
apparent existence may be due to an error in my typing of 0's and 1's.