Hamming Distance for Nominal Data

Hello world.!

I have two matrices [2 X 10] and [173 X 10] with each column being a nominal value,so I though that hamming distance could be appropriate.

Is it necessary to transform each column to binary representation or can I use it as is?Moreover, if it is necessary, does anyone know a way to trasform them and bring them back to the initial state?Because I know dummyvar, but not the way to reverse it.

Thank you all,

Andreas Kampianakis