Communications Toolbox

Representing Words for Reed-Solomon Codes

This toolbox supports Reed-Solomon codes that use m-bit symbols instead of bits. If you want to create an [n,k] Reed-Solomon code, then your message must be a k-column Galois array in the field GF(2^m). Each array entry must be an integer between 0 and 2^m-1. The code corresponding to that message is an n-column Galois array in GF(2^m). The codeword length n must be between 3 and 2^m-1.

Note    For information about Galois arrays and how to create them, see Representing Elements of Galois Fields or the reference page for the gf function.

The example below illustrates how to represent words for a [7,3] Reed-Solomon code.

• n = 7; k = 3; % Codeword length and message length
  m = 3; % Number of bits in each symbol
  msg = gf([1 6 4; 0 4 3],m); % Message is a Galois array.
  c = rsenc(msg,n,k) % Code will be a Galois array.
  

The output is

• c = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
   
  Array elements = 
   
       1     6     4     4     3     6     3
       0     4     3     3     7     4     7
  

Performing Other Binary Block Code Tasks

Parameters for Reed-Solomon Codes