Is there a name for the property of a code where symbol "space" is left unused?

Question

For example, say I have the symbols A, B, C and D.

If I encode these as A = 1, B = 01, C = 001 and D = 0001 (for a very simple example), I have a very simple prefix code. However, I know straight away that it cannot be optimal. Instead of using D = 0001, I could have used D = 000 and retained the prefix property.

The second case (A = 1, B = 01, C = 001 and D = 000) could potentially be a Huffman code and may be optimal (or may not) depending on the probabilities of the symbols A, B, C and D.

My question is, is there a name for the property that distinguishes this second case from the first, not assuming anything about whether the second code is optimal or not?

Thanks in advance, and sorry for the confusing title.

Answer 1

It seems if all space is used, the code is called a complete code. I don't know the main source of the definition but it was used here: If Kraft's inequality holds with equality, the code in question is a complete code.