Arithmetic in Galois Fields :: Galois Field Computations (Communications Toolbox)

Communications Toolbox

Arithmetic in Galois Fields

You can perform arithmetic operations on Galois arrays by using familiar MATLAB operators, listed in the table below. Whenever you operate on a pair of Galois arrays, both arrays must be in the same Galois field.

Operation	Operator
Addition	`+`
Subtraction	`-`
Elementwise multiplication	`.*`
Matrix multiplication	`*`
Elementwise left division	`./`
Elementwise right division	`.\`
Matrix left division	`/`
Matrix right division	`\`
Elementwise exponentiation	`.^`
Elementwise logarithm	`log()`
Exponentiation of a square Galois matrix by a scalar integer	`^`

Note For multiplication and division of polynomials over a Galois field, see Addition and Subtraction of Polynomials.

Examples of these operations are in the sections that follow:

Example: Addition and Subtraction
Example: Multiplication
Example: Division
Example: Exponentiation
Example: Elementwise Logarithm

Primitive Polynomials and Element Representations

Example: Addition and Subtraction