How is a one-hot code called, if zero is acepted, too?
This code is often used in FPGAs to encode state machines. Typically one bit will be used to encode each state.

It's not very efficient in the encoding, but then one-bit registers are a cheap resource. 

It is very efficient when decoding what to do, as if you can guarrantee that only one bit it hot, very little gating is needed.

It is extremely efficient is debugging, one state &lt;-> one bit really helps the human mind figure out what's going on.

In those circumstances, the '0000' encoding appears naturally for the 'power on' or 'idle' condition. I've not seen anybody feel the need to describe it as anything other than a 'one hot', as it's kid of obvious what's going on.n

If you really must, then you will want something that is as snappy as 'one hot', like perhaps 'one hot or not', 'none or one hot', 'one or none hot', but 'one hot with zeros' is pretty clear.