For a linear code C of length n and dimension k, Wolf noticed that the trellis state complexity s(C) of C is upper-bounded by := w(C) min(k, n - k). In this correspondence, we point out some new lower hounds for s(C). In particular, if C is an algebraic-geometric code, then s (C) greater than or equal to w (C) - (g - a), where g is the genus of the underlying curve and a is the abundance of the code.493733737