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

• prim_poly = [2 2 1];
  [polyformat, expformat] = gftuple([2 1],prim_poly,3)
  
  polyformat =
  
       2     1
  
  
  expformat =
  
       7
  

Example: Generating a List of Galois Field Elements

Arithmetic in Galois Fields