  The order bound for the minimum distance of algebraic geometry codes was
originally defined for the duals of one-point codes and later generalized for
arbitrary algebraic geometry codes. Another bound of order type for the minimum
distance of general linear codes, and for codes from order domains in
particular, was given in [H. Andersen and O. Geil, Evaluation codes from order
domain theory, Finite Fields and their Applications 14 (2008), pp. 92-123].
Here we investigate in detail the application of that bound to one-point
algebraic geometry codes, obtaining a bound $d^*$ for the minimum distance of
these codes. We establish a connection between $d^*$ and the order bound and
its generalizations. We also study the improved code constructions based on
$d^*$. Finally we extend $d^*$ to all generalized Hamming weights.
