To start we note that any bit string containing k bits can be used to represent a polynomial of degree k-1 with coefficients of 0 and 1

To start we note that any bit string containing k bits can be used to represent a polynomial of degree k-1 with coefficients of 0 and 1

For example the bit string

110001

represents the polynomial

f(x) = 1.x5 + 1.x4 + 0.x3 + 0.x2 + 0.x1 + 1.x0

= x5 + x4 + 1

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