A variation of this sometimes used is to label the elements of the basis by the elements , 0, 1, 2, ..., 6, of the projective line over the finite field of order 7. The multiplication is then given by and , and all expressions obtained from this by adding a constant (modulo 7) to all subscripts: in other words using the seven triples (124) (235) (346) (450) (561) (602) (013). These are the nonzero codewords of the quadratic residue code of length 7 over the Galois field of two elements, . There is a symmetry of order 7 given by adding a constant mod 7 to all subscripts, and also a symmetry of order 3 given by multiplying all subscripts by one of the quadratic residues 1, 2, 4 mod 7.