Abstract
We introduce a new sequence ? associated to a numerical semigroup similar to the ? sequence used to define the order bound on the minimum distance and to describe the Feng---Rao improved codes. The new sequence allows a nice description of the optimal one-point codes correcting generic errors and to compare them with standard codes and with the Feng---Rao improved codes. The relation between the ? sequence and the ? sequence gives a new characterization of Arf semigroups and it is shown that the ? sequence of a numerical semigroup unequivocally determines it.
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