What is "hexacode"

n. (context coding theory English) A particular linear code of length 6 and dimension 3.

In coding theory, the hexacode is a length 6 linear code of dimension 3 over the Galois field GF(4) = {0, 1, ω, ω} of 4 elements defined by

H = {(a, b, c, f(1), f(ω), f(ω)) : f(x) :  = ax + bx + c; a, b, c ∈ GF(4)}.
It is a 3-dimensional subspace of the vector space of dimension 6 over GF(4). Then H contains 45 codewords of weight 4, 18 codewords of weight 6 and the zero word. The full automorphism group of the hexacode is 3.S. The hexacode can be used to describe the Miracle Octad Generator of R. T. Curtis.