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

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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.

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Authors and Affiliations

  1. Universitat Rovira i Virgili, Tarragona, Catalonia, Spain

    Maria Bras-Amorós

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  1. Maria Bras-Amorós
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Correspondence to Maria Bras-Amorós.

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Communicated by Peter Wild.

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Bras-Amorós, M. On numerical semigroups and the redundancy of improved codes correcting generic errors. Des. Codes Cryptogr. 53, 111–118 (2009). https://doi.org/10.1007/s10623-009-9297-8

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  • DOI: https://doi.org/10.1007/s10623-009-9297-8

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