You can call it the cardinality (or size) of the support. It's typically associated with real-valued functions, but since zero and one are real values, treating this as a special case doesn't sound unreasonable to me. Support itself is a conveniently concise term, but would refer to the positions which are nonzero, not just the count.

You can call it the cardinality (or size) of the support. It's typically associated with real-valued functions, but since zero and one are real values, treating this as a special case doesn't sound unreasonable to me. Support itself is a conveniently concise term, but would refer to the positions which are nonzero, not just the count.

For example, assuming one-based indexing your $v=[1,0,0,1,0,1,1]$ has support $S=\{1,4,6,7\}$ since $v_i\neq 0$ for $i\in S$ and the size of that support is $\lvert S\rvert=4$.