Communications Toolbox

Polynomial Arithmetic

The functions gfadd and gfsub add and subtract, respectively, polynomials over GF(p). The gfconv function multiplies polynomials over GF(p). The gfdeconv function divides polynomials in GF(p), producing a quotient polynomial and a remainder polynomial. For example, the commands below show that 2 + x + x² times 1 + x over the field GF(3) is 2 + 2x² + x³.

• a = gfconv([2 1 1],[1 1],3)
  
  a =
  
       2     0     2     1
  
  [quot, remd] = gfdeconv(a,[2 1 1],3)
  
  quot =
  
       1     1
  
  remd =
  
       0
  

The previously discussed functions gfadd and gfsub add and subtract, respectively, polynomials. Because it uses a vector of coefficients to represent a polynomial, MATLAB does not distinguish between adding two polynomials and adding two row vectors elementwise.

Cosmetic Changes of Polynomials

Characterization of Polynomials