Communications Toolbox

Converting to Simplest Exponential Format

The same function gftuple also produces the simplest exponential representation of an element of GF(p^m), given either an exponential representation or a polynomial representation of that element. To retrieve this output, use the syntax

[polyformat, expformat] = gftuple(...)

The input format and the output polyformat are as in the table Behavior of gftuple Depending on Format of First Two Inputs . In addition, the variable expformat contains the simplest exponential format of the element represented in polyformat. It is simplest in the sense that the exponent is either -Inf or a number between 0 and p^m-2.

Example

To recover the exponential format of the element 2 + A that the previous section considered, use the commands below. In this case, polyformat contains redundant information, while expformat contains the desired result.

[polyformat, expformat] = gftuple([2 1],2,3)

polyformat =

     2     1

expformat =

     6

This output appears at first to contradict the information in the table Elements of GF(9) , but in fact it does not. The table uses a different primitive element; two plus that primitive element has the polynomial and exponential formats shown below.

prim_poly = [2 2 1];
[polyformat2, expformat2] = gftuple([2 1],prim_poly,3)

The output below reflects the information in the bottom line of the table.

polyformat2 =

     2     1


expformat2 =

     7

Example: Generating a List of Galois Field Elements

Arithmetic in Galois Fields

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