Hexacode

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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 of dimension 6 over . Then contains 45 codewords of weight 4, 18 codewords of weight 6 and the zero word. The full automorphism group of the hexacode is . The hexacode can be used to describe the Miracle Octad Generator of R. T. Curtis.

References[edit]

  • Conway, John H.; Sloane, Neil J. A. (1998). Sphere Packings, Lattices and Groups ((3rd ed.) ed.). New York: Springer-Verlag. ISBN 0-387-98585-9.