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Home > Vol 12, No 2 (2000)

E.R. van Dam and D. Fon-Der-Flaass

Let V and W be n-dimensional vector spaces over GF(2). A function Q : V Q(0) = 0; Q( x) + Q( y) + Q( z) + Q( x + y + z) \textonesuperior  0\text for any three distinct x, y, z; Q( x) + Q( y) + Q( z) + Q( x + a) + Q( y + a) + Q( z + a) \textonesuperior  0\text if a \textonesuperior  0\text ( x, y, z\text arbitrary). \begin{gathered} Q(0) = 0; \hfill \\ Q(x) + Q(y) + Q(z) + Q(x + y + z) \ne 0{\text{ for any three distinct }}x,y,z; \hfill \\ Q(x) + Q(y) + Q(z) + Q(x + a) + Q(y + a) + Q(z + a) \ne 0{\text{ if }}a \ne 0{\text{ }}(x,y,z{\text{ arbitrary}}). \hfill \\ \end{gathered}

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