Hexacode Explained
GF(4)=\{0,1,\omega,\omega2\}
of 4 elements defined by
H=\{(a,b,c,f(1),f(\omega),f(\omega2)):f(x):=ax2+bx+c;a,b,c\inGF(4)\}.
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 andthe zero word. The full
automorphism group of the hexacode is
. The hexacode can be used to describe the
Miracle Octad Generatorof R. T. Curtis.
References
- Book: Conway, John H. . John Horton Conway
. John Horton Conway . Sloane, Neil J. A. . Neil Sloane . 1998 . Sphere Packings, Lattices and Groups . registration . (3rd ed.) . Springer-Verlag . New York . 0-387-98585-9.
