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Open AccessArticle

Ideals of Numerical Semigroups and Error-Correcting Codes

Department of Computer Science and Mathematics, Universitat Rovira i Virgili, 43007 Tarragona, Catalonia, Spain
Symmetry 2019, 11(11), 1406; https://doi.org/10.3390/sym11111406
Received: 8 October 2019 / Revised: 6 November 2019 / Accepted: 11 November 2019 / Published: 14 November 2019
(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)
Several results relating additive ideals of numerical semigroups and algebraic-geometry
codes are presented. In particular, we deal with the set of non-redundant parity-checks, the code
length, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometry
codes from the perspective of the related Weierstrass semigroups. These results are related to
cryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, network
coding, and ramp secret sharing schemes. View Full-Text
Keywords: numerical semigroup; Weierstrass semigroup; semigroup ideal; error-correcting code; algebraic-geometry code numerical semigroup; Weierstrass semigroup; semigroup ideal; error-correcting code; algebraic-geometry code
MDPI and ACS Style

Bras-Amorós, M. Ideals of Numerical Semigroups and Error-Correcting Codes. Symmetry 2019, 11, 1406.

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