In coding theory, the hexacode is a length 6 linear code of dimension 3 over the Galois field of 4 elements defined by

It is a 3-dimensional subspace of the vector space contains 45 codewords of weight 4, 18 codewords of weight 6 and the zero word. The full automorphism group. The hexacode can be used to describe the Miracle Octad Generator of R. T. Curtis.

References