Girish Mahajan (Editor)

Hexacode

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In coding theory, the hexacode is a length 6 linear code of dimension 3 over the Galois field G F ( 4 ) = { 0 , 1 , ω , ω 2 } of 4 elements defined by

H = { ( a , b , c , f ( 1 ) , f ( ω ) , f ( ω 2 ) ) : f ( x ) := a x 2 + b x + c ; a , b , c G F ( 4 ) } .

It is a 3-dimensional subspace of the vector space of dimension 6 over G F ( 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 6 . The hexacode can be used to describe the Miracle Octad Generator of R. T. Curtis.

References

Hexacode Wikipedia