
210 Skewing Schemes
C, respectively, must be relatively prime to n to be conflict-free.
Let’s denote this as
gcd(A, n) = 1 , gcd(B, n) = 1 , gcd(C, n) = 1 .
Clearly, when n is prime, no matter which coefficients we use,
we get no conflict along the axis. For a standard chessboard (where
n = 8), however, there must be an odd number of coefficients so
no two entries will be mapped to the same module.
Now, to guarantee conflict-free diagonals requires us to consider
more than one axis or all the possible combinations of two or three
coefficients. First, let us consider diagonals within an orthogonal
slice of a cube, where only two axes change and one remains con- ...