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
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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Bras-Amorós, M. Ideals of Numerical Semigroups and Error-Correcting Codes. Symmetry 2019, 11, 1406.
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