[citation needed] The ternary Golay code consists of 36 = 729 codewords.

Every ternary word of length 11 has a Hamming distance of at most 2 from exactly one codeword.

The set of codewords with Hamming weight 5 is a 3-(11,5,4) design.

The complete weight enumerator of the extended ternary Golay code is The automorphism group of the extended ternary Golay code is 2.M12, where M12 is the Mathieu group M12.

The extended ternary Golay code can be constructed as the span of the rows of a Hadamard matrix of order 12 over the field F3.

Consider all codewords of the extended code which have just six nonzero digits.

The sets of positions at which these nonzero digits occur form the Steiner system S(5, 6, 12).

The three elements of the underlying finite field are represented here by

Products of these finite field elements are identical to those of the integers.

Row and column sums are evaluated modulo 3.

Linear combinations, or vector addition, of the rows of the matrix produces all possible words contained in the code.

The inner product of any two rows of the generator matrix will always sum to zero.

The matrix product of the generator and parity-check matrices,

It was independently discovered two years earlier by the Finnish football pool enthusiast Juhani Virtakallio, who published it in 1947 in issues 27, 28 and 33 of the football magazine Veikkaaja.

(Barg 1993, p.25) The ternary Golay code has been shown to be useful for an approach to fault-tolerant quantum computing known as magic state distillation.