On numerical semigroups and the redundancy of improved codes correcting generic errors
We introduce a new sequence tau associated to a numerical semigroup similar to the nu 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 tau sequence and the nu sequence gives a new characterization of Arf semigroups and it is shown that the tau sequence of a numerical semigroup unequivocally determines it.
numerical semigroup generic error algebraic code