How to make all possible changes of bits in a codeword?

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I have codeword u and I need to make a program that allows :
for 1<=i<=k ,make all possible changes of l of the k bits in u.

Example 1:

if u = [1 1 0 1] ; k = 4 and l = 1

we obtain :

u1 = [0 1 0 1] ; u2 = [1 0 0 1] ; u3 = [1 1 1 1] and u4 = [1 1 0 0].

Example 2 :

if u = [1 0 0 ] ; k = 3  and l = 1

we obtain :

u1 = [0 0 0] ; u2 = [1 1 0] and u3 = [1 0 1].

I tried to program, but i obtain :

if k = 3 and l = 1
u1 = [1 00] ; u2 = [010] and u3 = [001]

What I have tried:

My code :

l = 1;
ind = nchoosek(1:k, l);
t = size(ind,1);
u1 = zeros(t,k);
u1(bsxfun(@plus, (ind-1)*t, (1:t).')) = 1;

Posted 1-Jul-17 12:02pm

ChannelCoding

Updated 1-Jul-17 19:28pm

PIEBALDconsult

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PIEBALDconsult 1-Jul-17 19:49pm

Please use "Improve question" to explain what you are trying to do more clearly.

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RAMASWAMY EKAMBARAM · Answer 1 · 2017-07-01T19:28:00

I do not know MATLAB and your requirement is not very clear but the following C code achieves the output of the examples

C++

int u = 0x0d;   // 1101
int k = 4;
int l, result;

for(l = 1 << (k - 1); l != 0; l >>= 1)
{
	result = u ^ l; // 0101 = 1101 XOR 1000, 1001 = 1101 XOR 100, 1111 = 1101 XOR 10, 1100 = 1101 XOR 1
}
// it just remains to express 'result' in the form [b1 b2 b3 b4] - where b1 .. b4 are the bit values

the above code also works for second example with 3 bits with of course appropriate changes in value of u and k.