MATLAB: List all possible outcomes of 16 matches

Question

I am trying to make a code that will list all of the possible outcomes of 16 matches (only wins or losses, no draws), essentially the same as flipping a coin 16 times. I've tried using functions like combnk and nchoosek, but they cannot build a 16 column matrix with only two outcomes.

Ideally, the outcome would be a 16 X 4096 matrix (65,536 combinations) which would look like this

H H H H H H H H H H H H H H H H

H H H H H H H H H H H H H H H A

H H H H H H H H H H H H H H A H

And so on. Or, if the argument needed numbers, like this

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1

…

Thank you for your help!

Answer 1

dec2bin(0:2^16-1)-'0'