8.15 Polynomial arithmetic over {0,1}

The coefficients 0 and 1 are manipulated using the rules of Boolean arithmetic.

The following rules apply:

  • 0 + 0 = 1 + 1 = 0.

  • 0 + 1 = 1 + 0 = 1.

  • 0 * 0 = 0 * 1 = 1 * 0 = 0.

  • 1 * 1 = 1.

That is, adding two polynomials over {0,1} is the same as a bitwise exclusive OR, and multiplying two polynomials over {0,1} is the same as integer multiplication except that partial products are exclusive-ORed instead of being added.

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