CCS

Hamming Codes

Matlab Coding

 

% MATLAB script for Illustrative Problem 10.9.
echo on
k=11;
for i=1:2^k
    for j=k:-1:1
        if rem(i-1,2^(-j+k+1))>=2^(-j+k)
            u(i,j)=1;
        else
            u(i,j)=0;
        end
        echo off ;
    end
end
echo on ;

g=[1 0 0 0 0 0 0 0 0 0 0 1 1 0 0;
    0 1 0 0 0 0 0 0 0 0 0 0 1 1 0;
    0 0 1 0 0 0 0 0 0 0 0 0 0 1 1;
    0 0 0 1 0 0 0 0 0 0 0 1 0 1 0;
    0 0 0 0 1 0 0 0 0 0 0 1 0 0 1;
    0 0 0 0 0 1 0 0 0 0 0 0 1 0 1;
    0 0 0 0 0 0 1 0 0 0 0 1 1 1 0;
    0 0 0 0 0 0 0 1 0 0 0 0 1 1 1;
    0 0 0 0 0 0 0 0 1 0 0 1 0 1 1;
    0 0 0 0 0 0 0 0 0 1 0 1 1 0 1;
    0 0 0 0 0 0 0 0 0 0 1 1 1 1 1];

c=rem(u*g,2);
w_min=min(sum((c(2:2^k,:))'));

>> w_min

w_min =

3

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis