Multiplies elements of a finite field
c = gf_multiply(F, a, b)
A field created by gf_create_field.
Field elements.
In GF(p) (n = 1): a matrix of integers in 0 .. p-1, of any size.
In GF(p^n), n > 1: a matrix with n columns, one element per row. Each row holds the coefficients of a polynomial in α of degree < n, constant term first.
Coefficients outside 0 .. p-1 are rejected; reduce them first with gf_mod if needed.
The result, in the same form as the operands.
gf_multiply(F, a, b) computes a × b in the field F. For n > 1 the operands are multiplied as polynomials in α and the product is reduced modulo the field's primitive polynomial. In exponential notation, α^i × α^j = α^((i + j) mod (p^n - 1)).
Both operands must contain the same number of elements, or one of them must be a single element; a single element is combined with each element of the other operand. The result has the shape of the operand that holds several elements (of a when both have the same number).
F = gf_create_field(2, 4); a = [0 1 0 0]; // alpha b = [1 1 0 0]; // 1 + alpha = alpha^4 c = gf_multiply(F, a, b) // [0 1 1 0] gf_to_exponential(F, c) // 5 // alpha times alpha^0, alpha^1, alpha^2 gf_multiply(F, F(4)(2:4, :), a) P = gf_create_field(7, 1); gf_multiply(P, [3 4 5], 6) // [4 3 2] |  |  |
| Version | Description |
| 2.0.0 | Refactoring of the function/toolbox. Accepts several elements at once; invalid arguments raise errors. |