On numerical semigroups and the redundancy of improved codes correcting generic errors

Article

Abstract

We introduce a new sequence τ associated to a numerical semigroup similar to the ν 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 τ sequence and the ν sequence gives a new characterization of Arf semigroups and it is shown that the τ sequence of a numerical semigroup unequivocally determines it.

Keywords

Algebraic code Generic error Numerical semigroup 

Mathematics Subject Classifications (2000)

94B27 20M14 20M10 14G50 11T71 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Universitat Rovira i VirgiliTarragona, CataloniaSpain

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