The extended binary Golay code, G24 (sometimes just called the "Golay code" in finite group theory) encodes 12 bits of data in a 24-bit word in such a way that any 3-bit errors can be corrected or any 4-bit errors can be detected.

In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F242 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates.

That is, the spheres of radius three around code words form a partition of the vector space.

The other Mathieu groups occur as stabilizers of one or several elements of W. There is a single word of weight 24, which is a 1-dimensional invariant subspace.

There is an 11-dimensional invariant subspace, consisting of cocode words with odd weight, which gives

It is convenient to use the "Miracle Octad Generator" format, with coordinates in an array of 4 rows, 6 columns.

Griess (p. 59) uses the labeling: PSL(2,7) is naturally the linear fractional group generated by (0123456) and (0∞)(16)(23)(45).

There are 4 other code words of similar structure that complete the basis of 12 code words for this representation of W. W has a subspace of dimension 4, symmetric under PSL(2,7) x S3, spanned by N and 3 dodecads formed of subsets {0,3,5,6}, {0,1,4,6}, and {0,1,2,5}.

Hundreds of color pictures of Jupiter and Saturn in their 1979, 1980, and 1981 fly-bys would be transmitted within a constrained telecommunications bandwidth.

[9] The MIL-STD-188 American military standards for automatic link establishment in high frequency radio systems specify the use of an extended (24,12) Golay code for forward error correction.

[10][11] In two-way radio communication digital-coded squelch (DCS, CDCSS) system uses 23-bit Golay (23,12) code word which has the ability to detect and correct errors of 3 or fewer bits.