Hexacode
From Wikipedia, the free encyclopedia
In coding theory, the hexacode is length 6 linear code of dimension 3 over the Galois field GF(4) = {0,1,ω,ω2} of 4 elements defined by
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.S6. The hexacode can be used to describe the Miracle Octad Generator of R. T. Curtis.
[edit] References
- Conway, John H.; Sloane, Neil J. A. (1998). Sphere Packings, Lattices and Groups, (3rd ed.), New York: Springer-Verlag. ISBN 0-387-98585-9.
