The repo contains 2 version that can solve 1 norm regression.
The algorithm in one_norm.m can detect any conditions while the file OneNormLPxx.m may fail some cases. Becasue the 2nd version's assumption for non-degeneracy is too strong.
We need to run every combination of rows to make sure it's non-degenerate. This step is commented and don't use it for large cases.
To test code. Try random(30,40) to create a random generated 30x40 matrix and see the output.