Communications Toolbox

Multiplication and Division of Polynomials

To multiply and divide polynomials, use conv and deconv on Galois vectors that represent the polynomials. Multiplication and division of polynomials is equivalent to convolution and deconvolution of vectors. The deconv function returns the quotient of the two polynomials as well as the remainder polynomial. Examples are below.

m = 4;
apoly = gf([4 5 3],m); % A^2 x^2 + (A^2 + 1) x + (A + 1)
bpoly = gf([1 1],m); % x + 1
xpoly = gf([1 0],m); % x
% Product is A^2 x^3 + x^2 + (A^2 + A) x + (A + 1).
cpoly = conv(apoly,bpoly);
[a2,remd] = deconv(cpoly,bpoly); % a2==apoly. remd is zero.
[otherpol,remd2] = deconv(cpoly,xpoly); % remd is nonzero.

The multiplication and division operators in Arithmetic in Galois Fields multiply elements or matrices, not polynomials.

Addition and Subtraction of Polynomials

Evaluating Polynomials

© 1994-2005 The MathWorks, Inc.