More on the uniqueness of the Golay codes

AbstractIf C̄ is a set of 36 ternary vectors of length 12, distance ⩾6, containing 0, then we show that the supports of the weight 6 vectors in C̄ hold an S(5, 6, 12). Further we show that C̄ must be a linear, self-dual [12, 6, 6] code, hence the Golay code.Also any set C of 36 ternary vectors of length 11, distance ⩾5, containing 0, is linear and hence the Golay [11, 6, 6] code. The supports of the vectors of weight 5 in C hold an S(4, 5, 11).Similarities and differences with the binary case are discussed